On an order based construction of a groupoid from an inverse semigroup
| dc.creator | Lenz, Daniel | |
| dc.date | 2006-04-05 | |
| dc.date.accessioned | 2026-07-07T07:10:33Z | |
| dc.date.available | 2026-07-07T07:10:33Z | |
| dc.description | We present a construction, which assigns two groupoids, $\Gugamma$ and $\Gmgamma$, to an inverse semigroup $Γ$. By definition, $\Gmgamma$ is a subgroupoid (even a reduction) of $\Gugamma$. The construction unifies known constructions for groupoids. More precisely, the groupoid $\Gugamma$ is shown to be isomorphic to the universal groupoid of $Γ$ introduced by Paterson. For $Γ$ arising from graphs resp. tilings, the groupoid $\Gmgamma$ is the graph groupoid introduced by Kumjian et al. resp. the tiling groupoid introduced by Kellendonk. We obtain a characterisation of open invariant sets in $\Gmgamma^{(0)}$ in terms of certain order ideals of $\Gammanull$ for a large class of $Γ$ (including those arising from graphs and from tilings). If $\Gmgamma$ is essentially principal this gives a characterization of the ideal structure of $\Cred(\Gmgamma)$ by a theory of Renault. In particular, we then obtain necessary and sufficient conditions on $Γ$ for simplicity of $\Cred(\Gmgamma)$. Our approach relies on a detailed analysis of the order structure of $Γ$. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604105 | |
| dc.identifier | http://arxiv.org/abs/math/0604105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111453 | |
| dc.subject | Operator Algebras | |
| dc.subject | 22A22, 20M18, 18B35, 52C23 | |
| dc.title | On an order based construction of a groupoid from an inverse semigroup | |
| dc.type | text |