Simplicial homology of strong semilattices of Banach algebras

Details Simplicial homology of strong semilattices of Banach algebras Simplicial homology of strong semilattices of Banach algebras

2006-09-15

arxiv.org/abs/math/0609450v4

Houston J. Math. 36 (2010), no. 1, 237--260.

Mathematics

Functional Analysis

28 pages, final arXiv version. Slight improvement to abstract and MSC; minor changes to LaTeX (spacing, line breaks, use of do

Scientific paper

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.

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