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arXiv · 0709.3325

Hochschild homology and cohomology of {\ell}^1({\mathbb Z}_+^k)

Yemon Choi
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Abstract

Building on the recent determination of the simplicial cohomology groups of the convolution algebra ${\ell}^1({\mathbb Z}_+^k)$ [Gourdeau, Lykova, White, 2005] we investigate what can be said for cohomology of this algebra with more general symmetric coefficients. Our approach leads us to a discussion of Harrison homology and cohomology in the context of Banach algebras, and a development of some of its basic features. As an application of our techniques we reprove some known results on second-degree cohomology.

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Yemon Choi. 2008-09-02. Hochschild homology and cohomology of {\ell}^1({\mathbb Z}_+^k). https://doi.org/10.1093/qmath%2Fhan027

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