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

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

2007-11-23

arxiv.org/abs/0711.3669v3

Proc. Edinburgh Math. Soc. 53 (2010), no. 1, 97--109.

Mathematics

Functional Analysis

14pp, uses Paul Taylor's diagrams.sty macros. v3: typos caught and some minor corrections/clarifications of terminology. This

Scientific paper

10.1017/S0013091508000060

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.

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