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arXiv:math/0609450 [math.FA]AbstractReferencesReviewsResources

Simplicial homology of strong semilattices of Banach algebras

Yemon Choi

Published 2006-09-15, updated 2008-02-25Version 4

Certain semigroups are known to admit a `strong semilattice decomposition' into simpler pieces. We introduce a class of Banach algebras that generalise the $\ell^1$-convolution algebras of such semigroups, and obtain a disintegration theorem for their simplicial homology. Using this we show that for any Clifford semigroup $S$ of amenable groups, $\lp{1}(S)$ is simplicially trivial: this generalises results in \cite{YC_GMJ}. Some other applications are presented.

Comments: 28 pages, final arXiv version. Slight improvement to abstract and MSC; minor changes to LaTeX (spacing, line breaks, use of double subscripts, etc.); correction of a few more typos. A leaner version of this paper will appear in the Houston Journal of Mathematics
Journal: Houston J. Math. 36 (2010), no. 1, 237--260.
Categories: math.FA, math.CT, math.RA
Subjects: 46M20, 16E40, 43A20
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