$C^*$-algebras of inverse semigroups: amenability and weak containment
| dc.creator | Milan, David | |
| dc.date | 2006-10-10 | |
| dc.date | 2007-10-24 | |
| dc.date.accessioned | 2026-07-07T08:38:31Z | |
| dc.date.available | 2026-07-07T08:38:31Z | |
| dc.description | 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. | |
| dc.description | 14 pages. Corrected an error in Proposition 3.1 (thanks to the referee for finding this). This has led to a slight restructuring of the paper and an extra hypothesis in the main theorem | |
| dc.identifier | https://arxiv.org/abs/math/0610342 | |
| dc.identifier | http://arxiv.org/abs/math/0610342 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140755 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05; 20M18 | |
| dc.title | $C^*$-algebras of inverse semigroups: amenability and weak containment | |
| dc.type | text |