C^*-algebras of inverse semigroups: amenability and weak containment

2006/10/10 by David Milan, Milan, David
Mathematics · #20M18 #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.math/0610342

openalex publication_date 2006/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We argue that weak containment is an appropriate notion of amenability for inverse semigroups. Given an inverse semigroup S and a homomorphism ϕ of S onto a group G, we show, under an assumption on ker(ϕ), that S has weak containment if and only if G is amenable and ker(ϕ) has weak containment. Using Fell bundle amenability, we find a related result for inverse semigroups with zero. We show that all graph inverse semigroups have weak containment and that Nica's inverse semigroup \mcT_G,P of a quasi-lattice ordered group (G,P) has weak containment if and only if (G,P) is amenable.

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