Simplicial homology of strong semilattices of Banach algebras

• Autores: Yemon Choi
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 36, Nº 1, 2010, págs. 237-260
• Idioma: inglés
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• Resumen

  • 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.