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

Abstract

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.

arXiv comment14pp, 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