Infobox Radio Station image name WIUM airdate 1956 frequency 91.3 megahertz MHz area Illinois format Public broadcasting owner Western Illinois University erp 50.0 kW branding TriStates Public Radio callsign meaning W estern I llinois U niversity br M acomb slogan class B website http www.tristatesradio.com TriStates Radio WIUM 91.3 FM broadcasting FM is a 50,000 watt radio station in Macomb, Illinois , in west central Illinois . Western Illinois University is the station licensee, authorized by the Federal Communications Commission . Mission Tri States Public Radio is an outreach service of the College of Fine Arts and Communication at Western Illinois University. History prose date September 2008 1956 WWKS named for William Kimbrough Shake, who installed the equipment , signs on at 91.3 MHz ... 250 ft m sing on tower is constructed south of the building. 1970 WWKS becomes WIUM. 1978 WIUM ... Western Illinois University. 1981 WIUM relocates its transmitter to the new convert 500 ft m sing ... Broadcasting Service PBS Public television station WIUM TV , now Network Knowledge WMEC ... years. 1982 WIUM qualifies for Corporation for Public Broadcasting support and becomes a member ... in Sallee Hall . Image TriStates Coverage Map.jpg right thumb 300px WIUM & WIUW coverage map 1983 WIUM s first on air membership drive raises 3,550 in pledges. 1984 The station purchases its first compact disc player and begins 24 hour a day broadcasts. 1989 WIUM increases its power to 50,000 ... to public radio stations nationwide throughout the decade. 1991 WIUM s administrative reporting ... News Bureau in the Hotel Iowa in downtown Keokuk opens. 2005 WIUM become the first University licensed ... technology. External links FMQ WIUM TVQ WMEC http www.tristatesradio.com TriStates Radio http jrabold.net radio 7wium.shtml WIUM via streaming audio Allegro service NPR Illinois coord 40.428 N 90.683 W type landmark region US source FCC display title Category NPR member stations WIUM Category Radio ... more details
H kon Lie can refer to Haakon Lie , Norwegian politician H kon WiumLie , Norwegian technologist hndis Lie, Hakon Long comment to avoid being listed on short pages no H kon Lie ... more details
The Lie may refer to The Lie poem , political and social criticism poem probably written by Sir Walter Ralegh The Lie 1912 film , a silent film The Lie 1914 film , a silent film The Lie 2011 film , a dramatic film The Lie Evolution , a 1987 book by Ken Ham The Lie Lost , an episode of the television series Lost The Lie , a novel by Chad Kultgen . disambig es The Lie ... more details
Infobox single Name ... And That s No Lie Cover Heaven 17 and thats no lie single.jpg Artist Heaven 17 from Album How Men Are B side The Fuse Released 1985 in music 1985 Format 7 single, 12 single, cassette Recorded Genre Synth pop Length 3 25 Label Virgin Records Writer Glenn Gregory , Ian Craig Marsh , Martyn Ware Producer British Electric Foundation , Greg Walsh Last single This Is Mine br 1984 This single ... And That s No Lie br 1985 Next single The Foolish Thing To Do br 1986 ... And That s No Lie is synthpop trio Heaven 17 s first and only single music single of 1985 from the album How Men Are . ref cite web url http www.discogs.com Heaven 17 How Men Are master 62932 title Heaven 17 How Men Are at Discogs publisher Discogs.com date 2011 07 16 accessdate 2011 08 12 ref It was written by all three members. The single was released early 1984 and peaked at 52 in the UK, spending 5 weeks on the chart. ref cite web url http www.chartstats.com release.php?release 11985 title Heaven 17 And That s No Lie publisher Chart Stats date accessdate 2011 08 12 ref This was the band s first single to miss the top 50 since 1983. A promotional video was created for the single. Allmusic mentioned the track in the review of How Men Are , Highlights are numerous, including the very long but very wonderful And That s No Lie. A strong melody, stunning vocals from Glenn Gregory, and tight production ... url http www.discogs.com Heaven 17 And Thats No Lie release 2127641 title Heaven 17 ... And That s No Lie ... 17 song Temptation , I m Your Money and Play to Win . Formats 7 Single ... And That s No Lie 3 25 The Fuse 3 53 12 Single ... And That s No Lie Re mixed To Enhance Its Danceability 6 10 The Fuse L.P. version 3 05 ... And That s No Lie L.P. version 10 02 12 Single UK only ... And That s No Lie Re ... Promo Single That s No Lie 7 A 3 25 The Fuse 7 B 3 03 That s No Lie 12 A 6 10 The Fuse 3 03 That s No Lie ... 17 Megamix Sanny X References Reflist Heaven 17 DEFAULTSORT And That s No Lie Category 1985 ... more details
Otheruses Lie disambiguation Infobox film name L.I.E. image LIE Poster.png caption Theatrical release poster director Michael Cuesta producer Michael Cuesta br Linda Moran br Rene Bastian writer Stephen M. Ryder br Michael Cuesta br Gerald Cuesta starring Brian Cox actor Brian Cox br Paul Dano Paul Franklin Dano br Billy Kay actor Billy Kay music Pierre F ldes cinematography Romeo Tirone editing Eric Carlson br Kane Platt distributor New Yorker Films released start date 2001 1 20 runtime 108 minutes country filmUS language English budget 700,000 gross 1,667,192 L.I.E. is a 2001 American independent film about a relationship between Howie, a 15 year old boy, and a paedophile known as Big John . ref http www.nytimes.com 2001 09 16 movies film finding the wild heart of long island.html?pagewanted all New York Times review of L.I.E. ref The title is an acronym for the Long Island Expressway . The film was directed by Michael Cuesta , who has said that the film is about exploring sexuality. ref name ReferenceA Michael Cuesta Commentary issued as extra on DVD ref It stars Paul Dano Paul Franklin Dano as Howie and Brian Cox actor Brian Cox as Big John. Plot Unreferenced section date February 2010 Howie Blitzer Paul Dano Paul Franklin Dano is deeply affected by the death of his mother in a car accident on the Long Island Expressway , a situation made worse by his relationship with his distant father Marty Bruce Altman , who brought a trophy girlfriend into the house less than a month ... to be with him, sexually, or just father him . ref name ReferenceA NC 17 rating L.I.E. received an NC ... References reflist External links imdb title 0242587 amg movie 237133 mojo title lie http www.i reports.info m M200201.html L.I.E. at http www.i reports.info Interrogation Reports http www.metacritic.com movie lie critic reviews L.I.E. on Metacritic Category 2001 films Category 2000s drama films ... Category Independent films de L.I.E. Long Island Expressway fr L.I.E. it L.I.E. he ... more details
Single infobox Name LieLieLie Cover serj tankian lielie lie.png Artist Serj Tankian from Album Elect the Dead Released December 24, 2007 small Internet small br June 2008 small Radio small Format Music download Digital download , Compact disc CD Promotional recording Promo Recorded Genre Experimental rock , art rock , alternative metal Length 3 34 Label Serjical Strike Records Serjical Strike Reprise Records Reprise Writer Serj Tankian Producer Serj Tankian Last single Empty Walls br 2007 This single LieLieLie br 2007 For singles, we use the date that it was first released for the date. Next single Sky Is Over br 2008 Misc LieLieLie is a song by Serj Tankian . The song was released as a single from his debut solo debut album Elect the Dead . The music video is directed by Martha Colburn ref http soadfans.com Article540.htm Serj Tankian To Post Videos For Each Track On Forthcoming Solo Album ref . cquote At first I was skeptical because you have to adopt different roles simultaneously. You have to learn to self edit and fortunately I was able to be very critical. An example would be a song called LieLieLie , which is a funny a song but I had some very serious lyrics to it. Man, I went in there five fucking times trying to make that song great, but it just wasn t working. Then I realized the lyrics were way too serious for such a silly song. So I ripped them up, threw them on the floor and went in and did it all on the fly, just having fun and creating it all again from scratch. In the end the song became this really crazy, humorous drama. And you have to do that. You have to be critical and keep changing things until it sounds right. author Serj Tankian ref http soadfans.com ... la la la la la la la la lielielie either with Serj or by herself. The song is featured in the opening ... LieLieLie length1 3 34 References reflist Serj Tankian 2000s rock song stub Category 2008 singles it LieLieLie sv LieLieLie ... more details
wiktionary lie A lie is a type of deception, an untruth or telling the truth. Lie or LIE may also refer to Lie surname Lie Dream Theater single Lie Dream Theater Song Lie song Lie song , a song by Black Light Burns Lie The Love and Terror Cult , an album by Charles Manson Saint Lie Interstate 495 New York , also called the Long Island Expressway L.I.E. , a film revolving around the Long Island Expressway Law of iterated expectations or law of total expectation, a probability, statistical concept Lying position , the recumbent position of the human body Liechtenstein , IOC country code In socionics , a Logical Intuitive Extrovert Lie obstetrics , an obstetrical term for the axis of the foetus In mathematics named after Sophus LieLie algebra Lie bracket Lie derivative Lie group Group of Lie type Lie sphere geometry Lie theory Carath odory Jacobi Lie theorem See also Lye disambiguation disambig af Lie de Lie eo LIE fa fr Lie it LIE lt LIE ja LIE no Lie pt Lie sl Lie sv Lie efternamn ... more details
About the Norwegian politician the computer scientist H kon WiumLie Infobox person name Haakon Lie image H kon lie 2.jpg image size 200px caption birth date birth date 1905 9 22 df yes birth place Oslo ... occupation Party secretary for the Norwegian Labour Party 1945 1969 Haakon Lie 22 September 1905 ... in the party s history. Lie is widely considered along with Einar Gerhardsen to be the architect ... Communism communists . Lie remained active in Norwegian public life, even after his 100th ... to Trygve Lie , ref http dro.dur.ac.uk 115 1 56CMEIS.pdf The Oslo Agreement in Norwegian Foreign Policy pdf accessed 25.5.2009 ref Lie was the son of a fireman in Oslo then called Kristiania. Though ... 112 hours a week. ref name Bj rlo1 cite web url http www.arbark.no Utstilling Haakon Lie Haakon Lie01.htm title Et b l av vilje Haakon Lie et portrett page 1 publisher Labour Movement Archive and Library ... ref Lie got involved with the labour movement at the age of sixteen, in 1921. ref cite web url http www.dagsavisen.no kultur article298322.ece title Haakon Lie 101 forteller alt work Dagsavisen author ... Communist Party and the remaining Social democracy social democrats , Lie ended up on the latter wing .... ref name Bj rlo1 Image Lie, Tranmel & Gerhardsen.jpg left thumb 190px Left to right Haakon Lie , Martin ... created to promote education in the working class. ref name Bj rlo1 Lie has cited the AOF as the proudest ... than a simple right left one. ref name Bj rlo2 cite web url http www.arbark.no Utstilling Haakon Lie Haakon Lie02.htm title Et b l av vilje Haakon Lie et portrett page 2 publisher Labour Movement Archive ... point the former pacifist Lie also took flying lessons to actively participate in the conflict, but this plan ... World War II When Operation Weser bung Norway was invaded by Nazi Germany Germany in April 1940, Lie ... At this point further broadcasts became impossible, and Lie had to make his way south, through Finland ... This was followed by several high profile arrests among them Einar Gerhardsen and Lie had to flee ... more details
Lie bracket can refer to A bilinear binary operation the commutator defined on elements of a Lie algebra Lie bracket of vector fields mathdab Long comment to avoid being listed on short pages de Lie Klammer es Corchete de Lie nl Lie haak pl Nawias Liego ... more details
It s a Wonderful Lie may refer to It s a Wonderful Lie House It s a Wonderful Lie House , an episode of House, M.D. It s a Wonderful Lie , an List of The Fresh Prince of Bel Air episodes ep113 episode of The Fresh Prince of Bel Air It s a Wonderful Lie , an List of The Riches episodes ep12 episode of The Riches disambig ... more details
You Lie may refer to You Lie Reba McEntire song You Lie Reba McEntire song , from the album Rumor Has It You Lie The Band Perry song You Lie The Band Perry song , from the album The Band Perry You lie , a widely condemned Joe Wilson U.S. politician Outburst during 2009 Presidential address outburst by U.S. politician Joe Wilson disambiguation ... more details
The Biggest Lie may refer to The Biggest Lie , a song by H sker D from their 1984 album Zen Arcade The Biggest Lie , a song by Elliott Smith from his 1995 album Elliott Smith album Elliott Smith disambig ... more details
As a surname, Lie may refer to A Norwegian surname Lie , which may refer to Jonas Lie , Norwegian novelist Jonas Lie painter , Norwegian American painter Sophus Lie , Norwegian mathematician Trygve Lie , Norwegian politician, first Secretary General of the United Nations The common Chinese surname Li Li lang zh linktext , which is romanization of Chinese romanized Lie in some Minnan language s. See also Lie disambiguation surname Lie Category Chinese language surnames Category Norwegian language surnames ... more details
Lie groups In mathematics , a Lie algebra IPAc en icon l i , not IPAc en l a is an algebraic structure whose main use is in studying geometric objects such as Lie group s and differentiable manifold s. Lie algebras were introduced to study the concept of infinitesimal transformation s. The term Lie algebra after Sophus Lie was introduced by Hermann Weyl in the 1930s. In older texts, the name infinitesimal group is used. Definition and first properties A Lie algebra is a vector space math , mathfrak ... mathfrak g times mathfrak g to mathfrak g math called the Lie bracket , which satisfies the following ... ref For any associative algebra A with multiplication math math , one can construct a Lie algebra L A . As a vector space, L A is the same as A . The Lie bracket of two elements of L A is defined to be their commutator ... linear Lie algebra math mathfrak gl n F . math The associative algebra A is called an enveloping algebra of the Lie algebra L A . It is known that every Lie algebra can be embedded into one that arises ..., and ideals The Lie bracket is not an associative operation in general, meaning that math x ... in the theory of associative ring mathematics rings or associative algebra s is commonly applied to Lie algebras. A subspace math mathfrak h subseteq mathfrak g math that is closed under the Lie bracket is called a Lie subalgebra . If a subspace math I subseteq mathfrak g math satisfies a stronger condition that math mathfrak g ,I subseteq I, math then I is called an ideal in the Lie algebra math ... ideal in a Lie algebra coincide. ref A Lie algebra in which the commutator is not identically zero and which has no proper ideals is called simple . A homomorphism between two Lie algebras over the same ... of associative rings, ideals are precisely the kernels of homomorphisms, given a Lie algebra math ... isomorphism theorem holds for Lie algebras. Given two Lie algebras math mathfrak g math and math mathfrak g math , their Direct sum of modules direct sum is the Lie algebra consisting of the vector ... more details
Image Espen Lie NM Hamar 2007 nr 2.jpg thumb Espen Lie at the Norwegian Chess Championship at Hamar 2007 Espen Lie born January 3, 1984 is a Norway Norwegian chess player who currently holds the title of International Master , and was the Norwegian Chess Champion for 2007. He is the younger brother of GM Kjetil A. Lie . Lie plays for the chess club in Porsgrunn . In the 2007 Norwegian championship, played at Hamar , Espen Lie and Geir Sune Tallaksen also representing Porsgrunn shared first place with 6.5 points out of 9. The result was viewed as surprising, for Lie and Tallaksen were ranked as number 9 and 10 out of 20 in the tournament, behind a number of grandmasters. ref http www.nettavisen.no sjakk article1204564.ece Omkamp om kongepokalen Rematch for the royal trophy Nettavisen July 7, 2007 no icon ref A play off between the two was arranged September 21 23 in Porsgrunn to determine the champion, and Lie prevailed in the sixth game after the first five games all were drawn. ref http www.nettavisen.no sjakk article1349278.ece Espen Lie ny norgesmester Espen Lie new Norwegian Champion Nettavisen version of September 27, 2007, retrieved February 28, 2008 no icon ref Espen Lie has one GM norm, won after 5.5 9 in an international tournament in Reykjavik. ref http www.nettavisen.no sjakk article1674862.ece Ny milep l for Espen Lie New milestone for Espen Lie Nettavisen, March 12 2008 no icon ref Apart from chess, Lie s training to become a teacher. References references External links fide id 1502611 chessgames player id 49524 Persondata Metadata see Wikipedia Persondata . NAME Lie, Espen ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH January 3, 1984 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Lie, Espen Category 1984 births Category Norwegian chess players Category Chess International Masters Category Living people norway chess bio stub no Espen Lie sjakkspiller nn Espen Lie ... more details
Lie theory pronounced IPA en li respell LEE is an area of mathematics , developed initially by Sophus Lie . Early expressions of Lie theory are found in books composed by Lie with Friedrich Engel mathematician Friedrich Engel and Georg Scheffers from 1888 to 1896. In Lie s early work, the idea was to construct ... application that Lie had in mind was to the theory of differential equation s. On the model of Galois ... of symmetry , the whole area of ordinary differential equation s. The hope that Lie Theory ... made Lie theory a central chapter of contemporary mathematics. The fact that there is a good structure theory for Lie groups and their representations has made them integral to large parts of abstract ... s and in mathematical physics , and the subject has become a busy crossroads. Elementary Lie theory The one parameter group s are the first instance of Lie theory. The compact space compact case arises ... the Lie algebra parameters have names angle , hyperbolic angle , and slope . Using the appropriate ... planar decompositions polar decomposition . Any one of these decompositions, or Lie algebra renderings, may be necessary for rendering the Lie subalgebra of a 2 2 real matrix Read a matrix 2 2 real matrix . There is a classical 3 parameter Lie group and algebra pair the versor quaternions of unit length which can be identified with the 3 sphere . Its Lie algebra is the subspace of quaternion vectors. Since the commutator ij &minus ji 2k, the Lie bracket in this algebra is twice the cross ... group and its Lie algebra. Standard treatments of Lie theory often begin with the Classical group s. Aspects of Lie theory The foundation of Lie theory is the exponential map relating Lie algebra to Lie group . Structure is captured in Root system s and Root datum root data . Lie theory is frequently ... to Group of Lie type Groups of Lie type . In 1900 David Hilbert challenged Lie theorists with his .... See also List of Lie group topics References cite book first Thomas last Hawkins year 2000 ... more details
Vilhelm Gabriel Heiberg Lie 1877 1935 was a Norway Norwegian civil servant. He was a son of Emil Bernhard Lie 1836 1891 , a brother of Bernt Lie and a nephew of writer Jonas Lie . His father was a first cousin of Erika Nissen Erika Nissen and Ida Lie , and so Vilhelm was a second cousin of the children in the next generation Erika Lie , Karl Nissen , Michael Str m Lie , Mons Lie writer Mons Lie , Erik Lie writer Erik Lie , painter Jonas Lie painter Jonas Lie , ref name snl2 cite encyclopedia year 2007 title Lie slekt etter Mons Jonass n encyclopedia Store norske leksikon editor Henriksen, Petter publisher Kunnskapsforlaget location Oslo url http www.snl.no Lie slekt etter Mons Jonass C3 B8n language Norwegian accessdate 8 December 2010 ref and Eyolf Soot . ref http runeberg.org jonaslie 0021.html Uddrag af Sl gttavlen ref Together with Anna Benedicte Aars Nicolaysen 1880 1965 he had the son Nils Lie Nils Aars Nicolaysen Lie , a notable writer. ref cite encyclopedia year title Nils Lie encyclopedia Norsk biografisk leksikon first ystein last Rottem authorlink ystein Rottem editor Knut Helle Helle, Knut publisher Kunnskapsforlaget location Oslo url http www.snl.no .nbl biografi Nils Lie utdypning language Norwegian accessdate 8 December 2010 ref His son was a first cousin of Emil Lie , a second cousin of the Nazi Jonas Lie government minister Jonas Lie , and father of professor of medicine Mons Lie. ref name snl2 Vilhelm Lie took the cand.jur. degree in 1899. He was a tax collector in Bergen from 1914 to 1919, ref name arbleks cite encyclopedia year 1935 volume 5 title Lie, Vilhelm Gabriel Heiberg encyclopedia Arbeidernes Leksikon editor Jakob Friis Friis, Jakob Trond Hegna Hegna, Trond Dagfin Juel Juel, Dagfin publisher Arbeidermagasinets Forlag location Oslo language Norwegian ... . NAME Lie, Vilhelm ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1877 PLACE OF BIRTH DATE OF DEATH 1935 PLACE OF DEATH DEFAULTSORT Lie, Vilhelm Category 1877 births Category 1935 deaths Category ... more details
Infobox Album See Wikipedia WikiProject Albums Name LieLie Live Type EP Artist Serj Tankian Cover LieLie Live.jpg Caption Released July 1, 2008 Genre Alternative metal , experimental rock , art rock Length 21 07 Label Reprise Records Reprise Serjical Strike Records Serjical Strike Producer Serj Tankian Reviews Last album Elect the Dead br 2007 This album LieLie Live br 2008 Next album Elect the Dead Symphony br 2010 Misc LieLie Live is a music download digital download Extended play EP by System of a Down frontman, Serj Tankian exclusively on Rhapsody online music service Rhapsody featuring live tracks, and remixes. There is no known promo release of this EP, however Warner Chappell released a promo sampler containing all the remixes in unmastered form. Track listing tracklist all writing Serj Tankian title1 LieLieLie note1 Live from MySpace s The List length1 3 49 title2 The Unthinking Majority note2 Live from MySpace s The List length2 3 53 title3 Empty Walls note3 Victorious Club Mix length3 5 45 title4 Sky Is Over note4 Fawk Yeah Remix length4 3 39 title5 Empty Walls note5 Dub Remix length5 4 01 Personnel Live tracks Serj Tankian and The F.C.C. Serj Tankian Lead vocalist lead vocals , Musical keyboard keyboard s, synthesizer s Mario Pagliarulo Bass guitar bass , Backing vocalist backing vocals Erwin Khachikian keyboards, piano , synthesizers, backing vocals Troy Zeigler Drum kit drums , backing vocals Dan Monti guitar , backing vocals Larry LaLonde Larry Ler LaLonde guitar, backing vocals Remixes main Elect the Dead Personnel DJ LethalRush Empty Walls Victorious Club Mix References http www.rhapsody.com serjtankian lielielive Free Music LieLie Live by Serj Tankian Rhapsody Online Serj Tankian Category 2008 EPs cs LieLie Live it LieLie Live sv LieLie Live ... more details
Infobox ski jumper name H vard Lie image fullname nickname birth date Birth date and age 1975 5 21 df y birth place height club By sen IL skis personalbest seasons 1995 2003 wins 0 additionalpodiums 0 totalpodiums 0 H vard Lie born 21 May 1975 is a retired Norway Norwegian ski jumping ski jumper . In the Ski jumping World Cup World Cup he finished 3 times among the top 10. At the 1997 FIS Nordic World Ski Championships he finished 28th in the normal hill and 9th in the large hill. External links FIS S JP ID 35208 Persondata Metadata see Wikipedia Persondata . NAME Lie, Havard ALTERNATIVE NAMES SHORT DESCRIPTION Ski jumper DATE OF BIRTH 21 May 1975 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Lie, Havard Category 1975 births Category Living people Category Norwegian ski jumpers Norway skijumping bio stub de H vard Lie fr Haavard Lie it H vard Lie no H vard Lie nn H vard Lie pl H vard Lie ... more details
Infobox planet minorplanet yes width 25em bgcolour FFFFC0 apsis name 26955 Lie symbol image caption discovery yes discovery ref discoverer P. G. Comba discovery site Prescott Observatory Prescott discovered June 30, 1997 designations yes mp name 26955 alt names 1997 MR1 named after Sophus Lie mp category orbit ref epoch May 14, 2008 aphelion 2.5167871 perihelion 2.0829739 semimajor eccentricity 0.0943121 period 1273.9616257 avg speed inclination 23.64077 asc node 252.55315 mean anomaly 54.57943 arg peri 349.19141 satellites physical characteristics yes dimensions mass density surface grav escape velocity sidereal day axial tilt pole ecliptic lat pole ecliptic lon albedo temperatures temp name1 mean temp 1 max temp 1 temp name2 max temp 2 spectral type abs magnitude 14.7 26955 Lie 1997 MR1 is a Asteroid belt main belt asteroid discovered on June 30, 1997 by P. G. Comba at Prescott Observatory Prescott . It is named after the Norway Norwegian mathematician Sophus Lie . References Reflist External links http ssd.jpl.nasa.gov sbdb.cgi?sstr 26955 Lie JPL Small Body Database Browser on 26955 Lie Minor planets navigator 26954 Skadiang 26956 1997 MT3 Small Solar System bodies DEFAULTSORT Lie Category Main Belt asteroids Category Asteroids named for people Category Astronomical objects discovered in 1997 beltasteroid stub fa it 26955 Lie ja 26955 no 26955 Lie nn 26955 Lie pl 26955 Lie pt 26955 Lie uk 26955 vi 26955 Lie yo 26955 Lie ... more details
In mathematics , Lie algebroids serve the same role in the theory of Lie groupoid s that Lie algebra s serve in the theory of Lie groups reducing global problems to infinitesimal ones. Just as a Lie groupoid can be thought of as a Lie group with many objects , a Lie algebroid is like a Lie algebra with many objects . More precisely, a Lie algebroid is a triple math E, cdot, cdot , rho math consisting of a vector bundle math E math over a manifold math M math , together with a Lie bracket math cdot ... for all math X,Y in Gamma E math . Examples Every Lie algebra is a Lie algebroid over the one point manifold. The tangent bundle math TM math of a manifold math M math is a Lie algebroid for the Lie ... of the tangent bundle &mdash that is, one whose sections are closed under the Lie bracket &mdash also defines a Lie algebroid. Every bundle of Lie algebras over a smooth manifold defines a Lie algebroid where the Lie bracket is defined pointwise and the anchor map is equal to zero. To every Lie groupoid is associated a Lie algebroid, generalizing how a Lie algebra is associated to a Lie group see also below . For example, the Lie algebroid math TM math comes from the pair groupoid whose objects ... a Lie algebroid to a Lie groupoid is not always possible, ref Marius Crainic, Rui L. Fernandes. http arxiv.org abs math 0105033 Integrability of Lie brackets , Ann. of Math. 2 , Vol. 157 2003 , no. 2, 575 620 ref but every Lie algebroid gives a Algebraic stack stacky Lie groupoid. ref Hsian Hua Tseng and Chenchang Zhu, Integrating Lie algebroids via stacks, Compositio Mathematica, Volume 142 2006 ... Zhu, Lie II theorem for Lie algebroids via stacky Lie groupoids, Ann. of Math. 2 , Vol. 157 2003 ... of a Lie algebra g on a manifold M, the set of g invariant vector fields on M is a Lie algebroid ... P over a manifold M is a Lie algebroid with short exact sequence math 0 to P times G mathfrak g to TP G xrightarrow rho TM to 0. math The space of sections of the Atiyah algebroid is the Lie algebra ... more details
In mathematics , a Lie subgroup H of a Lie group G is a Lie group that is a subset of G and such that the inclusion map from H to G is an injective Immersion mathematics immersion and group homomorphism . According to Cartan s theorem , a closed subgroup of G admits a unique smooth structure which makes it an embedding embedded Lie subgroup of G i.e. a Lie subgroup such that the inclusion map is a smooth embedding. Examples of non closed subgroups are plentiful for example take G to be a torus of dimension 2, and let H be a one parameter subgroup of irrational slope , i.e. one that winds around in G . Then there is a Lie group homomorphism R G with H as its image. The closure topology closure of H will be a sub torus in G . In terms of the exponential map of G , in general, only some of the Lie subalgebras of the Lie algebra g of G correspond to closed Lie subgroups H of G . There is no criterion solely based on the structure of g which determines which those are. References Citation last1 Helgason first1 Sigurdur title Differential geometry, Lie groups, and symmetric spaces publisher American Mathematical Society location Providence, R.I. series Graduate Studies in Mathematics isbn 978 0 8218 2848 9 id MathSciNet id 1834454 year 2001 volume 34 Citation last1 Warner first1 Frank W. title Foundations of differentiable manifolds and Lie groups publisher Springer Verlag location New York Berlin Heidelberg series Graduate Texts in Mathematics isbn 978 0 3879 0894 6 id MathSciNet id 0722297 year 1983 volume 94 External links http mathworld.wolfram.com LieGroup.html Lie Group on Mathworld Category Lie groups ... more details
Use dmy dates date November 2011 Infobox scientist name Sophus Lie image Sophus Lie.jpg image size caption ... students known for Lie algebra s and Lie group s author abbreviation bot author abbreviation zoo prizes Lobachevsky Medal religion footnotes Marius Sophus Lie IPA sv li no Lee 17 December 1842 18 February ... Klein and they became close friends. When he left Berlin, Lie traveled to Paris, where he was joined ... to leave France very quickly. Lie decided then to visit Luigi Cremona in Milan but he was arrested ... was released from prison after a month, thanks to the intervention of Darboux. Lie obtained his PhD ... professorship for him. That same year, Lie visited Felix Klein Klein , who was then at University ... Lie proposed to Anna Birch, then eighteen years old, and they were married in 1874. The couple ... , by then . Engel would help Lie to write his most important treatise, Theorie der Transformationsgruppen ... be one of the two editors of Lie s collected works. In 1886 Lie became professor at University of Leipzig ... he suffered a mental breakdown and had to be hospitalized until June 1890. Lie resigned from his ... of Sciences National Academy of Sciences of the United States of America in 1895. Sophus Lie died ... . Legacy Lie s principal tool, and one of his greatest achievements, was the discovery that continuous transformation groups now called, after him, Lie group s could be better understood by linearizing them, and studying the corresponding generating vector field s the so called Lie group The Lie algebra associated to a Lie group infinitesimal generator s . The generators are subject to a linearized ... called a Lie algebra . ref name pdf Citation last Helgason first Sigurdur contribution Sophus Lie, the Mathematician contribution url http ocw.mit.edu courses mathematics 18 755 introduction to lie groups fall 2004 readings helga sopmath3 2.pdf title Proceedings of The Sophus Lie Memorial Conference ... postscript . ref ref name two Hermann Weyl used Lie s work on group theory in his papers from 1922 and 1923 ... more details
Orphan date August 2011 Hollywood Lie is a 2001 song performed by Norway Norwegian artist Hanah. The song peaked on 3 on the Norwegian chart and stayed on the chart for 12 weeks. ref http norwegiancharts.com showitem.asp?interpret Hanah&titel Hollywood Lie Hanah Hollywood Lie , norwegiancharts.com. Retrieved 23 May 2011. ref The song was later covered by Sweden Swedish artist Hannah Westin in Fame Factory . References references Category 2001 songs song stub ... more details
Lie groups In mathematics , a Lie group IPAc en icon l i is a group mathematics group which is also ... structure smooth structure . Lie groups are named after Sophus Lie , who laid the foundations of the theory of continuous transformation group s. Lie groups represent the best developed theory ... theory to the case of continuous symmetry groups was one of Lie s principal motivations. Overview Image Circle as Lie group.svg right thumb The circle of center 0 and radius 1 in the complex plane is a Lie group with complex multiplication. Lie groups are smooth manifold s and, therefore, can be studied ... of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its infinitesimal group and which has since become known as its Lie algebra . Lie groups play an enormous role in modern geometry , on several different ... G is a Lie group of local symmetries of a manifold. On a global level, whenever a Lie group group ... of continuous symmetries expressed via a Lie group action on a manifold places strong constraints on its geometry and facilitates global analysis analysis on the manifold. Linear actions of Lie groups ... Kolchin, Armand Borel and Claude Chevalley realised that many foundational results concerning Lie ... with analogues of Lie groups over adele ring s p adic Lie groups play an important role, via their connections with Galois representations in number theory. Definitions and examples A real Lie group ... noncompact real Lie group. This group is connected space disconnected it has two connected components ... matrices form a subgroup of GL sub 2 sub R , denoted by SO sub 2 sub R . It is a Lie group in its own right specifically, a one dimensional compact connected Lie group which is diffeomorphic to the circle ... group also forms an interesting example of a Lie group. All of the previous examples of Lie groups fall within the class of classical group s. Related concepts A complex Lie group is defined in the same ... more details
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