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

Yemon Choi

doi:10.1017/S0013091508000060

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

Functional Analysis 2010-01-16 v3 Group Theory

Authors: Yemon Choi

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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.

Keywords

simplicial cohomology augmentation ideals group algebra Hochschild cohomology discrete group bounded cohomology commutative-transitive

Cite

@article{arxiv.0711.3669,
  title  = {Simplicial cohomology of augmentation ideals in ${\ell}^1(G)$},
  author = {Yemon Choi},
  journal= {arXiv preprint arXiv:0711.3669},
  year   = {2010}
}

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

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

Abstract

Keywords

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