About: Iwahori–Hecke algebra

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In mathematics, the Iwahori–Hecke algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a deformation of the group algebra of a Coxeter group. Hecke algebras are quotients of the group rings of Artin braid groups. This connection found a spectacular application in Vaughan Jones' construction of new invariants of knots. Representations of Hecke algebras led to discovery of quantum groups by Michio Jimbo. Michael Freedman proposed Hecke algebras as a foundation for topological quantum computation.

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rdf:type	yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:Group100031264 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:Science105999797 yago:WikicatAlgebras yago:WikicatQuantumGroups
rdfs:label	Iwahori-Hecke-Algebra (de) Algèbre de Hecke (fr) Iwahori–Hecke algebra (en) ヘッケ環 (ja) 黑克代數 (zh)
rdfs:comment	Iwahori-Hecke-Algebren sind in der Mathematik unter anderem in der geometrischen Darstellungstheorie (etwa bei der Definition des Kazhdan-Lusztig-Polynoms) und in der Knotentheorie (bei der Definition des Jones-Polynoms) von Bedeutung. Iwahori-Algebren kommen klassisch als Endomorphismenringe in der Darstellungstheorie endlicher Chevalley-Gruppen vor, können aber für alle Coxeter-Gruppen definiert werden. Ihre komplexen Darstellungen hängen eng mit den Darstellungen der assoziierten Coxeter-Gruppen zusammen. (de) In mathematics, the Iwahori–Hecke algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a deformation of the group algebra of a Coxeter group. Hecke algebras are quotients of the group rings of Artin braid groups. This connection found a spectacular application in Vaughan Jones' construction of new invariants of knots. Representations of Hecke algebras led to discovery of quantum groups by Michio Jimbo. Michael Freedman proposed Hecke algebras as a foundation for topological quantum computation. (en) L′algèbre de Hecke est une déformation du groupe de Coxeter à un paramètre, qui présente un intérêt théorique dans l'étude des nœuds notamment au travers du polynôme de Jones : ces algèbres apparaissent comme quotients des algèbres de groupes de tresses artiniens. L'étude des représentations des algèbres de Hecke a permis à Michio Jimbo de formuler une théorie générale des groupes quantiques. En tant que déformations du groupe de Coxeter, on parle également d'algèbre d'Iwahori-Hecke, en l'honneur des mathématiciens Erich Hecke et (en). (fr) 数学における岩堀ヘッケ環あるいは単にヘッケ環（へっけかん、英語: Hecke algebra; ヘッケ代数）はコクセター群の群環の一径数変形版で、表現論における重要な対象である。ほかにも局所体上の簡約代数群の表現論や保型形式論、作用素環論において考察されるような、群とその部分群の対に付随する両側不変関数のなす畳み込み積環によって与えられる一連の系列がある。 A-型の岩堀ヘッケ環はアルティンの組紐群と密接な関係があり、ヴォーン・ジョーンズによる新しい結び目不変量の構成に応用がある。また、ヘッケ環の表現は神保道夫による量子群の発見を導いた。さらに、マイケル・フリードマンはヘッケ環をの基礎付けとして提示した。 (ja) 黑克代數，又名，是對稱羣環（group ring for the symmetric group）的形變，在代數數論及表示論都會出現。 (zh)
dcterms:subject	Algebras Representation theory
Wikipage page ID	521808 (xsd:integer)
Wikipage revision ID	1118571811 (xsd:integer)
Link from a Wikipage to another Wikipage	Andrey Zelevinsky Vaughan Jones Iwahori subgroup Michio Jimbo Algebras Compact support Continuous function Convolution Gelfand pair Neutral element Locally compact topological group Jones polynomial Laurent polynomial Local field Erich Hecke Finite field Length function Principal series representation Hecke operators Ivan Cherednik Jacques Tits Coxeter group Semisimple algebra Abstract algebra Representation theory Affine Hecke algebra Chevalley group Borel subgroup Philip Kutzko Group ring Michael Freedman Bruhat order Semilinear map Unimodular group Ian G. Macdonald Quantum group Topological quantum computer Nagayoshi Iwahori Residue field Weyl group Modular forms Affine Weyl group Affine quantum group Characteristic zero Colin Bushnell Artin braid group Coxeter system Reductive algebraic group Modular representation Kazhdan–Lusztig polynomials Macdonald's constant term conjecture dbr:Reduced_decomposition dbr:Theory_of_types_(mathematics)
Link from a Wikipage to an external page	http://www.numdam.org/item%3Fid=PMIHES_1965__25__5_0 https://books.google.com/books%3Fid=DRgM79-9qVcC&printsec=frontcover&dq=isbn:0521837030&hl=en&sa=X&ved=0ahUKEwiZqKLpyNDjAhVBYs0KHXVRBjkQ6AEIKjAA%23v=onepage&q=%22Iwahori%E2%80%93Hecke%22&f=false https://www.ams.org/bookstore-getitem/item=CRMM-18 https://www.ams.org/bookstore-getitem/item=ULECT-15 https://www.ams.org/online_bks/ulect4/
sameAs	Iwahori–Hecke algebra Iwahori–Hecke algebra Iwahori–Hecke algebra Iwahori–Hecke algebra Iwahori–Hecke algebra Iwahori–Hecke algebra Iwahori–Hecke algebra
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