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Simplicial cohomology of augmentation ideals in l1(G)

Part of: Homological methods Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  12 January 2010

Yemon Choi
Yemon Choi
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg R3T 2N2, Canada, Email: (y.choi.97@cantab.net)
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Abstract

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Let G be a discrete group.We give a decomposition theorem for the Hochschild cohomology of l1(G) with coefficients in certain G-modules. Using this we show that if G is commutative-transitive, the canonical inclusion of bounded cohomology of G into simplicial cohomology of l1(G) is an isomorphism.

Keywords

bounded cohomologysimplicial cohomologyBanach algebrascommutative-transitive group

MSC classification

Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 20E45: Conjugacy classes
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 1 , February 2010 , pp. 97 - 109
Copyright
Copyright © Edinburgh Mathematical Society 2010