Left regular representations of Garside categories I. C*-algebras and groupoids

Li, X. (2023) Left regular representations of Garside categories I. C*-algebras and groupoids. Glasgow Mathematical Journal, 65(S1), S53-S86. (doi: 10.1017/S0017089522000106)

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We initiate the study of C∗ -algebras and groupoids arising from left regular representations of Garside categories, a notion which originated from the study of Braid groups. Every higher rank graph is a Garside category in a natural way. We develop a general classification result for closed invariant subspaces of our groupoids as well as criteria for topological freeness and local contractiveness, properties which are relevant for the structure of the corresponding C∗ -algebras. Our results provide a conceptual explanation for previous results on gauge-invariant ideals of higher rank graph C∗ -algebras. As another application, we give a complete analysis of the ideal structures of C∗ -algebras generated by left regular representations of Artin–Tits monoids.

Item Type:Articles
Additional Information:This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 817597).
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:Glasgow Mathematical Journal
Publisher:Cambridge University Press
ISSN (Online):1469-509X
Published Online:25 April 2022
Copyright Holders:Copyright © 2022 The Author
First Published:First published in Glasgow Mathematical Journal 65(S1): S53-S86
Publisher Policy:Reproduced under a Creative Commons licence

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
311039IGOCXin LiEuropean Commission (EC)N/AM&S - Mathematics