Semi-infinite cohomology and Hecke algebras

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dc.creatorSevostyanov, A.
dc.date2000-04-21
dc.date.accessioned2026-07-07T04:34:50Z
dc.date.available2026-07-07T04:34:50Z
dc.descriptionThis paper provides a homological algebraic foundation for generalizations of classical Hecke algebras introduced in math.QA/9805134. These new Hecke algebras are associated to triples of the form (A,B,e), where A is an associative algebra containing subalgebra B with character e. These algebras are connected with cohomology of associative algebras in the sense that for every left A-module V and right A-module W the Hecke algebra associated to triple (A,B,e) naturally acts in the B-cohomology and B-homology spaces of V and W, respectively. We also introduce the semi-infinite cohomology functor for associative algebras and define modifications of Hecke algebras acting in semi-infinite cohomology spaces. We call these algebras semi-infinite Hecke algebras. As an example we realize the W-algebra W(g) associated to a complex semisimple Lie algebra g as a semi-infinite Hecke algebra. Using this realization we explicitly calculate the algebra W(g) avoiding the bosonization technique used by Feigin and Frenkel.
dc.description45 pages, AMSLaTeX, 1 figure using XY-pic
dc.identifierhttps://arxiv.org/abs/math/0004139
dc.identifierhttp://arxiv.org/abs/math/0004139
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59058
dc.subjectRings and Algebras
dc.subjectCategory Theory
dc.subjectRepresentation Theory
dc.subject16E40 (Primary) 17B55 17B67 (Secondary)
dc.titleSemi-infinite cohomology and Hecke algebras
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