Simplicial homology of strong semilattices of Banach algebras
Abstract
Certain semigroups are known to admit a `strong semilattice decomposition' into simpler pieces. We introduce a class of Banach algebras that generalise the 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, 1(S) is simplicially trivial: this generalises results in YCGMJ. Some other applications are presented.
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