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On semi-infinite cohomology of finite-dimensional graded algebras

Part of: Groups and algebras in quantum theory Homological methods Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  23 February 2010

Roman Bezrukavnikov  and
Leonid Positselski
Roman Bezrukavnikov
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (email: bezrukav@math.mit.edu)
Leonid Positselski
Affiliation:
Sector of Algebra and Number Theory, Institute for Information Transmission Problems, Moscow 127994, Russia (email: posic@mccme.ru)
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Abstract

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We describe a general setting for the definition of semi-infinite cohomology of finite-dimensional graded algebras, and provide an interpretation of such cohomology in terms of derived categories. We apply this interpretation to compute semi-infinite cohomology of some modules over the small quantum group at a root of unity, generalizing an earlier result of Arkhipov (posed as a conjecture by B. Feigin).

Keywords

semi-infinite cohomologysmall quantum groups

MSC classification

Secondary: 16E30: Homological functors on modules (Tor, Ext, etc.) 17B37: Quantum groups (quantized enveloping algebras) and related deformations 81R50: Quantum groups and related algebraic methods
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 2 , March 2010 , pp. 480 - 496
Copyright
Copyright © Foundation Compositio Mathematica 2010

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