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Rights statement: http://journals.cambridge.org/action/displayJournal?jid=GMJ The final, definitive version of this article has been published in the Journal, Glasgow Mathematical Journal, 48 (2), pp 231-245 2006, © 2006 Cambridge University Press.

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Simplicial homology and Hochschild cohomology of Banach semilattice algebras

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Journal publication date 05/2006 Glasgow Mathematical Journal 2 48 15 231-245 Published English

Abstract

The $\ell^{1}$-convolution algebra of a semilattice is known to have trivial cohomology in degrees 1, 2 and 3 whenever the coefficient bimodule is symmetric. We extend this result to all cohomology groups of degree $\geq 1$ with symmetric coefficients. Our techniques prove a stronger splitting result, namely that the splitting can be made natural with respect to the underlying semilattice.

Bibliographic note

http://journals.cambridge.org/action/displayJournal?jid=GMJ The final, definitive version of this article has been published in the Journal, Glasgow Mathematical Journal, 48 (2), pp 231-245 2006, © 2006 Cambridge University Press.