In mathematics , a linear representation &rho of a group G is a monomial representation if there is a finite index subgroup H and a one dimensional linear representation &sigma of H , such that &rho is equivalent to the induced representation Ind sub H sub sup G sup &sigma . Alternatively, one may define it as a representation whose image is in the monomial matrices . Here for example G and H may be finite group s, so that induced representation has a classical sense. The monomial representation is only a little more complicated than the permutation representation of G on the coset s of H . It is necessary only to keep track of scalars coming from &sigma applied to elements of H . References Springer id m m064780 title Monomial representation Category Representation theory of groups Algebra stub it Rappresentazione monomiale ... more details
Symbolic representation may refer to Symbolism disambiguation Symbolic linguistic representation In politics, it has to do with a representative in congress or in a group that is seen as being there to represent a group of minorities whether it be gender or cultural groups. See also Symbolic disambiguation Representation disambiguation disambig ... more details
precise machine format representation of decimal quantities. As compared to typical binary formats ... 3 5 7 9 5 6 8 9 8 11 15 Since BCD is a form of decimalrepresentation, several of the digit sums above ... decimal exponent. For example, 0.2 can be represented as 2 e 1 . This representation allows rapid ... and electronics electronic systems, binary coded decimal BCD is a digital encoding method for numbers using decimal notation, with each decimal digit represented by its own Binary numeral system binary ..., represent the decimal range 0 through 9. Other bit patterns are sometimes used for a Sign mathematics ... early decimal computer s. Although BCD is not as widely used as in the past, decimal Fixed point ... decimal title General Decimal Arithmetic ref Basics As described in the introduction, BCD takes advantage of the fact that any one decimal numeral can be represented by a four bit pattern border 1 cellpadding 2 cellspacing 0 align center width 30 bgcolor E0E0E0 width 50 Decimal br Digit bgcolor ... numeral in the most significant nibble bits 4 7 . As an example, encoding the decimal number tt 91 tt using uncompressed BCD results in the following binary pattern of two bytes Decimal 9 1 Binary 0000 1001 0000 0001 In packed BCD, the same number would fit into a single byte Decimal 9 1 ..., to represent the decimal number tt 12345 tt in packed BCD, using big endian format, a program would encode as follows Decimal 1 2 3 4 5 Binary 0000 0001 0010 0011 0100 0101 Note that the most significant ... when representing numbers internally in BCD format, since a conversion from or to binary representation ... decimal , which has been in use since the 1960s or earlier and implemented in all IBM mainframe hardware since then. In most representations, one or more bytes hold a decimal integer, where each of the two nibble s of each byte represent a decimal digit, with the more significant digit in the upper ... significant digits of the packed decimal value. The lower nibble of the rightmost byte is usually ... more details
In mathematics , if G is a group mathematics group and &rho is a linear representation of it on the vector space V , then the dual representation Overline &rho is defined over the dual vector space Overline V as follows ref Lecture 1 of Fulton Harris ref Overline &rho g is the transpose of a linear map transpose of &rho g sup &minus 1 sup for all g in G . Then Overline &rho is also a representation, as may be checked explicitly. The dual representation is also known as the contragredient representation . If math mathfrak g math is a Lie algebra and &rho is a representation of it over the vector space V , then the dual representation Overline &rho is defined over the dual vector space Overline V as follows ref Lecture 8 of Fulton Harris ref Overline &rho u is the transpose of &minus &rho u for all u in math mathfrak g math . Overline &rho is also a representation, as can be explicitly checked. For a unitary representation , the conjugate representation and the dual representation coincide, up to equivalence of representations. Generalization A general ring Module mathematics module does not admit a dual representation. Modules of Hopf algebra s do, however. See also Complex conjugate representation Kirillov Character Formula References references Category Representation theory of groups fr Repr sentation duale ... more details
Unreferenced date December 2009 Orphan date December 2009 This article addresses the notion of quasiregularity in the context of representation theory and topological algebra . For other notions of quasiregularity in mathematics , see the disambiguation page quasiregular . In mathematics, quasiregular representation is a concept of representation theory, for a locally compact group G and a homogeneous space G H where H is a closed subgroup . In line with the concepts of regular representation and induced representation , G acts on functions on G H . If however Haar measure s give rise only to a quasi invariant measure on G H , certain correction factors have to be made to the action on functions, for L sup 2 sup G H to afford a unitary representation of G on square integrable function s. With appropriate scaling factors, therefore, introduced into the action of G , this is the quasiregular representation or modified induced representation. DEFAULTSORT Quasiregular Representation Category Unitary representation theory Category Topological groups ... more details
distinguish Trivial module In the mathematics mathematical field of representation theory , a trivial representation is a group representationrepresentation math V , &phi of a Group mathematics group G on which all elements of G act as the identity mapping of V . A trivial Representation mathematics representation of an associative algebra associative or Lie algebra is a Lie algebra representation Lie algebra representation for which all elements of the algebra act as the zero linear map endomorphism which sends every element of V to the zero vector . For any group or Lie algebra, an irreducible representation irreducible trivial representation always exists over any field, and is one dimensional, hence unique up to isomorphism. The same is true for associative algebras unless one restricts attention to unital algebra s and unital representations. Although the trivial representation is constructed in such a way as to make its properties seem tautologous, it is a fundamental object of the theory. A subrepresentation is equivalent to a trivial representation, for example, if it consists of invariant vectors so that searching for such subrepresentations is the whole topic of invariant theory . The trivial character is the character mathematics character that takes the value of one for all group elements. References Fulton Harris . Category Representation theory algebra stub zh ... more details
context date February 2012 unreferenced date February 2012 Politics Models of representation refer to ways in which elected officials behave in representative democracy representative democracies . There are three types delegate , trustee , and politician politico . See also Delegate model of representation Trustee model of representation Category Democracy ... more details
In mathematics , in the representation theory of algebraic group s, a linear representation of an algebraic group is said to be rational if, viewed as a map from the group to the general linear group, it is a rational map of algebraic varieties. Finite direct sums and products of rational representations are rational. A rational math G math module is a module that can be expressed as a sum not necessarily direct of rational representations. see Group representation References http www.jstor.org view 00029327 di994362 99p00143 Extensions of Representations of Algebraic Linear Groups http www.encyclopediaofmath.org index.php Rational representation Springer Online Reference Works Rational Representation Category Representation theory of algebraic groups algebra stub ... more details
In mathematics , especially in the area of abstract algebra known as representation theory , a faithful representation of a group mathematics group G on a vector space V is a linear representation in which different elements g of G are represented by distinct linear mappings g . In more abstract language, this means that the group homomorphism G GL V is injective . Caveat While representations of G over a field K are de facto the same as math K G math modules with math K G math denoting the Group ring Group algebra over a finite group group algebra of the group G , a faithful representation of G is not necessarily a faithful module for the group algebra. In fact each faithful math K G math module is a faithful representation of G , but the converse does not hold. Consider for example the natural representation of the symmetric group S sub n sub in n dimensions by permutation matrices , which is certainly faithful. Here the order of the group is n while the n × n matrices form a vector space of dimension n sup 2 sup . As soon as n is at least 4, dimension counting means that some linear dependence must occur between permutation matrices since 24 16 this relation means that the module for the group algebra is not faithful. Properties A representation V of a finite group G over an algebraically closed field K of characteristic zero is faithful as a representation if and only if every irreducible representation of G occurs as a subrepresentation of S sup n sup V the n th symmetric power of the representation V for a sufficiently high n . Also, V is faithful as a representation if and only if every irreducible representation of G occurs as a subrepresentation of math V otimes n underbrace V otimes V otimes cdots otimes V n text times math the n th tensor power of the representation V for a sufficiently high n . References Springer id F f038170 title faithful representation Category Representation theory algebra stub ... more details
A representation term is a word, or a combination of words, used as part of a data element name . Representation class is sometimes used as a synonym for representation term. In ISO IEC 11179 , a representation class provides a way to Taxonomic classification classify or group data element s. A representation class is effectively a specialized classification scheme . Hence, there is currently some discussion in ISO over the merits of keeping representation class as a separate entity in 11179, versus collapsing it into the general classification scheme facility ref Issue114 . A clear distinction between the two mechanisms, however, is that 11179 allows a data element to be classified by only one representation class, whereas there is no such restriction on other classification schemes. ISO IEC 11179 does not specify that representation terms should be drawn from the values of representation class , though it would make sense to do so, nor does it provide any mechanism to ensure any sort of consistency whatever that might mean between the representation terms used to name a data element, and the representation class used to classify it. The term representation class has been used in metadata ... light on the semantics or meaning of the data element. Definitions of representation class There are several alternate definitions for representation class . Some of these are taken from the ISO documents ... rules. ISO Definitions of representation class From ISO IEC TR 20943 1 First edition 2003 08 01 pdf page 91 B.2.3 Representation class Representation class is the value domain for representation. The set ... element categorized with the representation class amount is different from an element categorized as number ... using them together. Representation class is a mechanism by which the functional and or presentational ... 02 15 3.3.51 data element representation class the class of representation of a data element See also ... to the ISO bugzilla discussion of Representation class External links http standards.iso.org ittf PubliclyAvailableStandards ... more details
In mathematics mathematical field of representation theory , a quaternionic representation is a group representationrepresentation on a complex number complex vector space V with an invariant quaternionic ... the division algebra of quaternion s . From this point of view, quaternionic representation of a group ... quaternion linear transformations of V . In particular, a quaternionic matrix representation of g ... concepts If V is a unitary representation and the quaternionic structure j is a unitary operator, then V admits an invariant complex symplectic form &omega , and hence is a symplectic representation . This always holds if V is a representation of a compact group e.g. a finite group and in this case ..., amongst irreducible representation s, can be picked out by the Frobenius Schur indicator . Quaternionic representations are similar to real representation s in that they are isomorphic to their complex conjugate representation . Here a real representation is taken to be a complex representation with an invariant ... satisfies math j 2 1. , math A representation which is isomorphic to its complex conjugate, but which is not a real representation, is sometimes called a pseudoreal representation . Real and pseudoreal ... algebra R G . Such a representation will be a direct sum of central simple R algebras, which, by the Artin ... a real or pseudoreal representation is a direct sum of irreducible real representations and irreducible .... Examples A common example involves the quaternionic representation of rotation s in three ... multiplication. By restricting this to the unit quaternions, we obtain a quaternionic representation of the spinor group Spin 3 . This representation &rho Spin 3 &rarr GL 1, H also happens to be a unitary quaternionic representation because math rho g dagger rho g mathbf 1 , math for all g in Spin 3 . Another unitary example is the spin representation of Spin 5 . An example of a nonunitary quaternionic representation would be the two dimensional irreducible representation of Spin 5,1 . More generally ... more details
In the mathematics mathematical field of representation theory a real representation is usually a group representationrepresentation on a real number real vector space U , but it can also mean a representation on a complex number complex vector space V with an invariant real structure , i.e., an antilinear ... C is a representation on a complex vector space with an antilinear equivariant map given by complex conjugation . Conversely, if V is such a complex representation, then U can be recovered as the fixed ... concretely in terms of matrices, a real representation is one in which the entries of the matrices ... column vectors. A real representation on a complex vector space is isomorphic to its complex conjugate representation , but the converse is not true a representation which is isomorphic to its complex conjugate but which is not real is called a pseudoreal representation . An irreducible pseudoreal representation V is necessarily a quaternionic representation it admits an invariant quaternionic ... real nor quaternionic in general. A representation on a complex vector space can also be isomorphic to the dual representation of its complex conjugate. This happens precisely when the representation ... of the representation and is the Haar measure with G 1. For a finite group, this is given by math ... is 1, then the representation is real. If the indicator is zero, the representation is complex hermitian , ref Any complex representation V of a compact group has an invariant hermitian form ... form on V . ref and if the indicator is &minus 1, the representation is quaternionic. Examples All representation of the symmetric group symmetric groups are real and in fact rational , since we can ... products of copies of the fundamental representation, which is real. Further examples of real ... see spin representation . Notes reflist 1 References Fulton Harris . citation first Jean Pierre ... 387 90190 6 . Category Representation theory pt Representa o real ... more details
In mathematical finite group theory, the vertex of a representation of a finite group is a subgroup associated to it, that has a special representation called a source . Vertices and sources were introduced by harvs txt last Green year 1959 References Citation last1 Green first1 J. A. title On the indecomposable representations of a finite group doi 10.1007 BF01558601 mr 0131454 year 59 month 1958 journal Mathematische Zeitschrift issn 0025 5874 volume 70 pages 430 445 Category Representation theory Category Finite groups ... more details
Self representation may refer to Self image Self portrait Pro se legal representation in the United States disambig Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. ... more details
In mathematics mathematical field of representation theory , a symplectic representation is a group representationrepresentation of a group mathematics group or a Lie algebra representation Lie algebra on a symplectic vector space V , which preserves the symplectic form . Here is a nondegenerate skew symmetric bilinear form math omega colon V times V to mathbb F math where F is the field mathematics field of scalars. A representation of a group G preserves if math omega g cdot v,g cdot w omega v,w math for all g in G and v , w in V , whereas a representation of a Lie algebra g preserves if math omega xi cdot v,w omega v, xi cdot w 0 math for all in g and v , w in V . Thus a representation of G or g is equivalently a group or Lie algebra homomorphism from G or g to the symplectic group Sp V , or its Lie algebra sp V , If G is a compact group for example, a finite group , and F is the field of complex numbers, then by introducing a compatible unitary structure which exists by an averaging argument , one can show that any complex symplectic representation is a quaternionic representation . Quaternionic representations of finite or compact groups are often called symplectic representations, and may be identified using the Frobenius Schur indicator . References Fulton Harris . Category Representation theory Category Symplectic geometry algebra stub it Rappresentazione simplettica ro Reprezentare simplectic ... more details
Unreferenced stub auto yes date December 2009 Orphan date November 2006 Substantive representation in contrast to descriptive representation is a concept in the legislative branch es of Representation politics representative republic s describing the tendency of representatives to advocate for certain groups. Often, their area of advocacy is in contrast to their background, such as late United States U.S. United States Senate Senator Ted Kennedy Edward Kennedy s advocacy for the poor Kennedy was a scion of one of the richest families in Massachusetts . Constituents vote for representatives by looking at policy stances and past efforts as a representative. DEFAULTSORT Substantive Representation Category Political terms Poli term stub ... more details
An affine representation of a topological group topological Lie group Lie group G on an affine space A is a continuity topology continuous smooth function smooth group homomorphism from G to the automorphism group of A , the affine group Aff A . Similarly, an affine representation of a Lie algebra g on A is a Lie algebra homomorphism from g to the Lie algebra aff A of the affine group of A . An example is the action of the Euclidean group E n upon the Euclidean space E sup n sup . Since the affine group in dimension n is a matrix group in dimension n 1, an affine representation may be thought of as a particular kind of linear representation . We may ask whether a given affine representation has a fixed point mathematics fixed point in the given affine space A . If it does, we may take that as origin and regard A as a vector space in that case, we actually have a linear representation in dimension n . This reduction depends on a group cohomology question, in general. See also Group action Projective representation References citation first1 Elisabeth last1 Remm first2 Michel last2 Goze title Affine Structures on abelian Lie Groups arxiv math 0105023 journal Linear Algebra and its Applications volume 360 year 2003 pages 215&ndash 230 doi 10.1016 S0024 3795 02 00452 4 . Category Group theory Category Homological algebra Category Representation theory Category Representation theory of Lie algebras Category Representation theory of Lie groups algebra stub eo Afina prezento pt Representa o afim ... more details
Adaptive representation is an extension by Francis Heylighen ref Heylighen, Francis 1990 . Representation and Change A Metarepresentational Framework for the Foundations of Physical and Cognitive Science . Communication and Cognition, Ghent, Belgium. ref to Kant s epistemology theory of knowledge . According to Kant, perception passes by the filters of the mind who observes the phenomena. In this line, there exists in the human mind invariant and a priori principles of experience. As an example, one may have imprinted in the brain a Dualism philosophy of mind Cartesian representation of space, a notion of time, color separation and others. This may be called static representation . Heylighen has proposed a revision of these Kantian ideas, in which these principles are not supposed to be invariant and necessary A priori and a posteriori philosophy a priori instead alternative principles exist for the organization of experience in adaptive representations. This opens a path for new investigations in the philosophy of mind and human cognition . References reflist External links http pcp.vub.ac.be books Rep&Change.pdf Web edition of Representation and Change 1999 . Epistemology stub Category Epistemology ... more details
In representation theory of Lie group s and Lie algebra s, a fundamental representation is an irreducible finite dimensional representation of a semisimple Lie algebra semisimple Lie group or Lie algebra whose highest weight is a fundamental weight . For example, the defining module of a classical Lie group is a fundamental representation. Any finite dimensional irreducible representation of a semisimple Lie group or Lie algebra can be constructed from the fundamental representations by a procedure due to lie Cartan . Thus in a certain sense, the fundamental representations are the elementary building blocks for arbitrary finite dimensional representations. Examples In the case of the general linear group , all fundamental representations are exterior power s of the defining module. In the case of the special unitary group SU n SU n , the n &minus 1 fundamental representations are the wedge products math operatorname Alt k mathbb C n math consisting of the alternating tensor s, for k 1, 2, ..., n &minus 1. The spin representation of the twofold cover of an odd orthogonal group , the odd spin group , and the two half spin representations ... that cannot be realized in the space of tensors. The adjoint representation of the simple Lie group of type E8 mathematics E sub 8 sub is a fundamental representation. Explanation The Representation ... group are indexed by their highest weight representation theory weights . These weights are the lattice ... and extract one copy of the irreducible representation corresponding to that dominant weight. Other uses Outside of Lie theory, the term fundamental representation is sometimes loosely used to refer to a smallest dimensional faithful representation, though this is also often called the standard or defining representation a term referring more to the history, rather than having a well defined mathematical meaning . References Fulton Harris Category Lie groups Category Representation theory algebra ... more details
for regular irreducible representations of a finite group Gelfand Graev representation In mathematics , and in particular the theory of group representation s, the regular representation of a group G is the linear representation afforded by the group action of G on itself by Translation group theory translation . One distinguishes the left regular representation given by left translation and the right regular representation given by the inverse of right translation. Finite groups For a finite group G , the left regular representation over a field mathematics field K is a linear representation ... by g , i.e. math lambda g h mapsto gh, text for all h in G. math For the right regular representation , an inversion must occur in order to satisfy the axioms of a representation. Specifically, given ... that the regular representation is generalized to topological group s such as Lie group ... representation of a group To say that G acts on itself by multiplication is tautological. If we consider this action as a group action permutation representation it is characterised as having ... representation of G , for a given field K , is the linear representation made by taking this permutation representation as a set of basis vector s of a vector space over K . The significance is that while the permutation representation doesn t decompose it is group action transitive the regular representation in general breaks up into smaller representations. For example if G is a finite group and K is the complex number field, the regular representation decomposes as a direct sum of representations direct sum of irreducible representation s, with each irreducible representation appearing ... to the number of conjugacy class es of G . The article on group algebra s articulates the regular representation for finite group s, as well as showing how the regular representation can be taken to be a module ... sum decomposition of the regular representation contains a representative of every isomorphism ... more details
In mathematics , the coadjoint representation &rho of a Lie group G is the dual representation dual of the adjoint representation of a Lie group adjoint representation . Therefore, if g denotes the Lie algebra of G , it is the action of G on the dual space to g . More geometrically, G acts by conjugacy class conjugation on its cotangent space at the identity element e , and this linear representation is &rho . Another geometrical interpretation is as the action by left translation on the space of right invariant 1 form s on G . The importance of the coadjoint representation was emphasised by work of Alexandre Kirillov , who showed that for nilpotent Lie group s G a basic role in their representation theory is played by coadjoint orbit . A coadjoint orbit O x for x in the dual space g of g may be defined either extrinsically, as the actual orbit group theory orbit G . x inside g , or intrinsically as the homogeneous space G H where H is the Group action Orbits and stabilizers stabilizer of x this distinction is worth making since the embedding of the orbit may be complicated. The coadjoint orbits are all symplectic manifold s with a natural 2 form inherited from g . In the Kirillov method of orbits representations of G are constructed geometrically starting from the coadjoint orbits. In some sense those play a substitute role for the conjugacy class es of G , which again may be complicated, while the orbits are relatively tractable. See also Borel Bott Weil theorem , for G a compact group Kirillov character formula Kirillov orbit theory References planetmath reference id 4760 title Coadjoint representation Category Representation theory of Lie groups Category Symplectic geometry ... more details
In the mathematics mathematical field of representation theory , a projective representation of a group mathematics group G on a vector space V over a field mathematics field F is a group homomorphism from G to the projective linear group PGL V , F GL V , F F sup &lowast sup where GL V , F is the general linear group of invertible linear transformations of V over F and F sup sup here is the normal ... representations and projective representations One way in which a projective representation can arise is by taking a linear group representation of G on V and applying the quotient map GL V , F &rarr ... given a projective representation , try to lift it to a conventional linear representation . File Projective representation lifting.svg 225px thumb A projective representation of G can be pulled back to a linear representation of a central extension C of G. In general, given a projective representation math rho colon G to operatorname PGL V math it cannot be lifted to a linear representation ... via group homology, as described below. However, one can lift a projective representation of G to a linear representation of a different group C, which will be a central extension mathematics ... the projective representation math rho colon G to operatorname PGL V math along the quotient map, obtaining a linear representation math sigma colon C to operatorname GL V , math and C will be a central ... extended we can speak of a linear representation of the extended group, which gives back the initial projective representation on factoring by F sup sup and the extending subgroup. The solution ... that the irreducible representation s of central extensions of G , and the irreducible projective representations of G , describe essentially the same questions of representation theory. Projective representations ... Press year 2006 isbn 978 0521835312 See also Affine representation Group action Category Homological algebra Category Group theory Category Representation theory Category Representation theory of groups ... more details
In the mathematics mathematical field of representation theory , group representations describe abstract ... that system. The term representation of a group is also used in a more general sense to mean any description of a group as a group of transformations of some mathematical object. More formally, a representation ... is a vector space we have a linear representation . Some people use realization for the general notion and reserve the term representation for the special case of linear representations. The bulk of this article describes linear representation theory see the last section for generalizations. Branches of group representation theory The representation theory of groups divides into subtheories ... divides the order of the group, then this is called modular representation theory this special case has very different properties. See Representation theory of finite groups . Compact group s or locally compact group s &mdash Many of the results of finite group representation theory are proved by averaging ..., so the results of compact representation theory apply to them. Other techniques specific ..., and their representation theory is crucial to the application of group theory in those fields. See ... groups is too broad to construct any general representation theory, but specific special cases .... Representation theory also depends heavily on the type of vector space on which the group acts ... A representation of a group mathematics group G on a vector space V over a field mathematics ... of a vector space general linear group on V . That is, a representation is a map math rho colon G to GL ... Here V is called the representation space and the dimension of V is called the dimension of the representation. It is common practice to refer to V itself as the representation when the homomorphism is clear ... , a continuous representation of G on V is a representation such that the application math Phi G times ... of a representation of a group G is defined as the normal subgroup of G whose image under ... more details
A representation term is a word, or a combination of words, that semantically represent the data type value domain of a data element. A representation term is commonly referred to as a class word by those familiar with data dictionary data dictionaries . ISO IEC 11179 5 2005 defines representation term as a designation of an instance of a representation class As used in ISO IEC 11179 , the representation ... type. A Representation class is a class of representations. This representation class provides a way to Taxonomic classification classify or group data element s. A Representation Term may be thought ... to the type of data stored in the data element. ref reptermasattr Representation terms are typically ... Element Framework uses a subset of CCTS representation terms and assigns numeric codes to those used. Use cases for representation term Managing Value Domains A value domain expresses the set of allowed values for a data element. The representation term and typically the corresponding data type term comprise a taxonomy for the value domains within a data set. This taxonomy is the representation class. Thus the representation term can be used to control proliferation of value domains by ensuring equivalent value domains use the same representation term. Finding equivalent properties When a person or software agent is analyzing two separate metadata registries to find property equivalence , the Representation ... terms i.e. Sex or Gender is much more efficient in this respect. Inference The Representation Term can be used in many ways to do inferences on data sets. Representation Terms tells the observer of any ... two distinct records. Required fields Representation Terms are also used to make inferences ... analyst looks at the Representation Terms to quickly find the dimensions and measures of a subject ... UN Core Components Technical Specification formally define both the allowed set of representation ... models for a wide variety of uses. In ISO 15000 5, the representation term provides a mechanism to harmonize ... more details
In mathematics the Burau representation is a group representationrepresentation of the braid group s, named after and originally studied by the German mathematician Werner Burau ref name burau cite journal last Burau first Werner year 1936 title ber Zopfgruppen und gleichsinnig verdrillte Verkettungen journal Abh. Math. Sem. Hamburg volume 11 pages 179 186 ref during the 1930s. The Burau representation has two common and near equivalent formulations, the reduced and unreduced Burau representations ... H 1 tilde P n math , and this representation is called the reduced Burau representation . The unreduced Burau representation has a similar definition, namely one replaces math P n math with its blowing ... x n 0 math , and math B n math acts on math Bbb Z n math by the permutation representation. Relation ... representation of the braid math f math . Faithfulness The first nonfaithful Burau representations are found .... Moody , http www.jstor.org pss 2159956 The faithfulness question for the Burau representation, Proc. AMS 1993 ref A more conceptual understanding ref name lp D D Long, M Paton, The Burau representation ... representation is unitary journal Proceedings of the American Mathematical Society volume 90 ... Paton theorem to show that the Burau representation is not faithful for n 5 ref name bigelow cite journal last Bigelow first Stephen year 1999 title The Burau representation is not faithful for n ... representations of the braid groups, Bourbaki 1999 2000 ref The Burau representation for n 2, 3 has been known to be faithful for some time. The faithfulness of the Burau representation when n 4 is an open problem. Geometry Squier showed that the Burau representation preserves a sesquilinear ... complex number near math 1 math it is a positive definite Hermitian pairing, thus the Burau representation can be thought of as a map into the Unitary group . References reflist DEFAULTSORT Burau Representation Category Braid groups Category Representation theory ... more details
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