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On graded centres and block cohomology

Part of: Representation theory of groups Homological methods

Published online by Cambridge University Press:  28 May 2009

Markus Linckelmann
Markus Linckelmann
Affiliation:
Department of Mathematical Sciences, Meston Building, University of Aberdeen, Aberdeen AB24 3UE, UK; Email: ([email protected])
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Abstract

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We extend the group theoretic notions of transfer and stable elements to graded centres of triangulated categories. When applied to the centre Z*(Db(B) of the derived bounded category of a block algebra B we show that the block cohomology H*(B) is isomorphic to a quotient of a certain subalgebra of stable elements of Z*(Db(B)) by some nilpotent ideal, and that a quotient of Z*(Db(B)) by some nilpotent ideal is Noetherian over H*(B).

Keywords

graded mapscentreblockcohomology

MSC classification

Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 20C20: Modular representations and characters
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 2 , June 2009 , pp. 489 - 514
Copyright
Copyright © Edinburgh Mathematical Society 2009