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Journal of Operator Theory

Volume 63, Issue 2, Spring 2010  pp. 317-332.

C-algebras of inverse semigroups: amenability and weak containment

Authors David Milan
Author institution: Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0130, U.S.A.

Summary:  We argue that weak containment is an appropriate notion of am\-enability 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 \mcTG,P of a quasi-lattice ordered group (G,P) has weak containment if and only if (G,P) is amenable.


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