Journal of Operator Theory
Volume 63, Issue 2, Spring 2010 pp. 317-332.
C∗-algebras of inverse semigroups: amenability and weak containmentAuthors: 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.
Contents Full-Text PDF