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Simplicial homology of strong semilattices of banach algebras

Lookup NU author(s): 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 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 results in [3]. Some other applications are presented. © 2010 University of Houston.

Publication metadata

Author(s): Choi Y

Publication type: Article

Publication status: Published

Journal: Houston Journal of Mathematics

Year: 2010

Volume: 36

Issue: 1

Pages: 237-260

Print publication date: 01/01/2010

ISSN (print): 0362-1588

ISSN (electronic):

Publisher: University of Houston

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