Home > Research > Publications & Outputs > Hochschild homology and cohomology of $\ell^1(\... ### Associated organisational units ### Links ### Text available via DOI: ## Hochschild homology and cohomology of$\ell^1(\mathbb Z_+^k)\$

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Journal publication date 2010 The Quarterly Journal of Mathematics 1 61 28 1-28 Published Undefined/Unknown

### Abstract

Building on the recent determination of the simplicial cohomology groups of the convolution algebra ℓ1(ℤk+) [F. Gourdeau, Z. A. Lykova and M. C. White, A Künneth formula in topological homology and its applications to the simplicial cohomology of ℓ1(ℤk+), Studia Math. 166 (2005), 29–54], we investigate what can be said for the cohomology of this algebra with more general symmetric coefficients. Our approach leads us to a discussion of the 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.