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Simplicial homology of strong semilattices of Banach algebras

Yemon Choi
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Abstract

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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Yemon Choi. 2008-02-25. Simplicial homology of strong semilattices of Banach algebras. https://arxiv.org/abs/math/0609450

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