Simplicial homology of strong semilattices of Banach algebras
arXiv:math/0609450
Abstract
Certain semigroups are known to admit a `strong semilattice decomposition' into simpler pieces. We introduce a class of Banach algebras that generalise the -convolution algebras of such semigroups, and obtain a disintegration theorem for their simplicial homology. Using this we show that for any Clifford semigroup of amenable groups, $\lp{1}(S)$ is simplicially trivial: this generalises results in \cite{YC_GMJ}. Some other applications are presented.
arXiv comment28 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