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Simplicial homology of strong semilattices of Banach algebras

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>2010
<mark>Journal</mark>Houston Journal of Mathematics
Issue number1
Volume36
Number of pages24
Pages (from-to)237-260
Publication StatusPublished
<mark>Original language</mark>English

Abstract

Certain semigroups are known to admit a 'strong semilattice decomposition' into simpler pieces. We introduce a class of Banach algebras that generalise the l1-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, l1(S) is simplicially trivial: this generalises previous results of the author (Glasgow Math. Journal, 2006). Some other applications are presented.