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

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.

arXiv commentv2: 36 pages, submitted. Abstract added, MSC-classes updated, typos corrected. Presentation trimmed a little. v3: 36 pages; further typos caught, added hyperlinks. Uses Paul Taylor's diagrams.sty macros. Leaner and rearranged version to appear in Q. J. Math. (Oxford)

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