|
In mathematics, the Iwahori–Hecke algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a one-parameter 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. ==Hecke algebras of Coxeter groups== Start with the following data: * (''W'', ''S'') is a Coxeter system with the Coxeter matrix ''M'' = (''m''''st''), * ''R'' is a commutative ring with identity. * is a family of units of ''R'' such that ''qs'' = ''qt'' whenever ''s'' and ''t'' are conjugate in ''W'' * ''A'' is the ring of Laurent polynomials over Z with indeterminates ''qs'' (and the above restriction that ''qs'' = ''qt'' whenever ''s'' and ''t'' are conjugated), that is ''A'' = Z () 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Iwahori–Hecke algebra」の詳細全文を読む スポンサード リンク
|