Partial transformation groupoids attached to graphs and semigroups

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)

210210.pdf - Accepted Version



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
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 (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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