Cartan subalgebras in uniform Roe algebras

White, S. and Willett, R. (2020) Cartan subalgebras in uniform Roe algebras. Groups, Geometry and Dynamics, 14(3), pp. 949-989. (doi: 10.4171/GGD/570)

Abstract

In this paper we study structural and uniqueness questions for Cartan subalgebras of uniform Roe algebras. We characterise when an inclusion B⊆A of C∗-algebras is isomorphic to the canonical inclusion of ℓ∞(X) inside a uniform Roe algebra C∗u(X) associated to a metric space of bounded geometry. We obtain uniqueness results for `Roe Cartans' inside uniform Roe algebras up to automorphism for non-amenable spaces X with property A, and up to inner automorphism when X has finite decomposition complexity.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: White, Professor Stuart
• Authors: White, S., and Willett, R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Groups, Geometry and Dynamics
• Publisher: European Mathematical Society
• ISSN: 1661-7207
• ISSN (Online): 1661-7215
• Published Online: 21 October 2020
• Copyright Holders: Copyright © 2020 European Mathematical Society
• First Published: First published in Groups, Geometry and Dynamics 14(3): 949-989
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

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Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
301348	0	von Neumann techniques in C*- algebras and dynamics	Stuart White	Engineering and Physical Sciences Research Council (EPSRC)	EP/R025061/1	M&S - Mathematics