Simplicial homology of strong semilattices of Banach algebras

Choi, Yemon (2010) Simplicial homology of strong semilattices of Banach algebras. Houston Journal of Mathematics, 36 (1). pp. 237-260.

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.