Li, X. (2017) Partial transformation groupoids attached to graphs and semigroups. International Mathematics Research Notices, 2017(17), pp. 5233-5259. (doi: 10.1093/imrn/rnw166)
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Abstract
We introduce the notion of continuous orbit equivalence for partial dynamical systems, and give an equivalent characterization in terms of Cartan-isomorphisms for partial C*-crossed products. Both graph C*-algebras and semigroup C*-algebras can be described as C*-algebras attached to partial dynamical systems. As applications, for graphs, we generalize and explain a result of Matsumoto and Matui relating orbit equivalence and Cartan-isomorphism, and for semigroups, we strengthen several structural results for semigroup C*-algebras concerning amenability, nuclearity as well as simplicity of boundary quotients. We also discuss pure infiniteness for partial transformation groupoids arising from graphs and semigroups.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Li, Professor Xin |
| Authors: | Li, X. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | International Mathematics Research Notices |
| Publisher: | Oxford University Press |
| ISSN: | 1073-7928 |
| ISSN (Online): | 1687-0247 |
| Published Online: | 02 August 2016 |
| Copyright Holders: | Copyright © 2016 The Author |
| First Published: | First published in International Mathematics Research Notices 2017(17): 5233-5259 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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