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Hochschild homology and cohomology of $\ell^1(\mathbb Z_+^k)$

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>2010
<mark>Journal</mark>The Quarterly Journal of Mathematics
Issue number1
Number of pages28
Pages (from-to)1-28
Publication StatusPublished
<mark>Original language</mark>Undefined/Unknown


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.