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Semigroup C*-algebras arising from graphs of monoids

Chen, C. and Li, X. (2023) Semigroup C*-algebras arising from graphs of monoids. International Mathematics Research Notices, (doi: 10.1093/imrn/rnac332) (Early Online Publication)

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Abstract

We study groupoids and semigroup C∗-algebras arising from graphs of monoids, in the setting of right LCM monoids. First, we establish a general criterion when a graph of monoids gives rise to a submonoid of the fundamental group that is right LCM. Moreover, we carry out a detailed analysis of structural properties of semigroup C∗-algebras arising from graphs of monoids, including closed invariant subspaces and topological freeness of the groupoids, as well as ideal structure, nuclearity, and K-theory of the semigroup C∗-algebras. As an application, we construct families of pairwise nonconjugate Cartan subalgebras in every UCT Kirchberg algebra.

Item Type:Articles
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Chen, Cheng and Li, Professor Xin
Authors: Chen, C., and 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:14 December 2022
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