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arXiv:0711.3669 [math.FA]AbstractReferencesReviewsResources

Simplicial cohomology of augmentation ideals in ${\ell}^1(G)$

Yemon Choi

Published 2007-11-23, updated 2008-08-14Version 3

Let $G$ be a discrete group. We give a decomposition theorem for the Hochschild cohomology of $\ell^1(G)$ 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 $\ell^1(G)$ is an isomorphism.

Comments: 14pp, uses Paul Taylor's diagrams.sty macros. v3: typos caught and some minor corrections/clarifications of terminology. This is not the final version, which will appear in Proc. Edinburgh Math. Soc
Journal: Proc. Edinburgh Math. Soc. 53 (2010), no. 1, 97--109.
Categories: math.FA, math.GR
Subjects: 16E40, 43A20, 20E45
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