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)

Abstract

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).
• 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: Glasgow Mathematical Journal
• Publisher: Cambridge University Press
• ISSN: 0017-0895
• 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

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
311039		IGOC	Xin Li	European Commission (EC)	N/A	M&S - Mathematics