Cartan subalgebras in C*-algebras. Existence and uniqueness

Li, X. and Renault, J. (2019) Cartan subalgebras in C*-algebras. Existence and uniqueness. Transactions of the American Mathematical Society, 372(3), pp. 1985-2010. (doi: 10.1090/tran/7654)

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We initiate the study of Cartan subalgebras in C*-algebras, with a particular focus on existence and uniqueness questions. For homogeneous C*-algebras, these questions can be analyzed systematically using the theory of fiber bundles. For group C*-algebras, while we are able to find Cartan subalgebras in C*-algebras of many connected Lie groups, there are classes of (discrete) groups, for instance non-abelian free groups, whose reduced group C*-algebras do not have any Cartan subalgebras. Moreover, we show that uniqueness of Cartan subalgebras usually fails for classifiable C*-algebras. However, distinguished Cartan subalgebras exist in some cases, for instance in nuclear uniform Roe algebras.

Item Type:Articles
Additional Information:The first named author was supported by EPSRC grant EP/M009718/1.
Glasgow Author(s) Enlighten ID:Li, Professor Xin
Authors: Li, X., and Renault, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Transactions of the American Mathematical Society
Publisher:American Mathematical Society
ISSN (Online):1088-6850
Published Online:12 April 2019
Copyright Holders:Copyright © 2019 American Mathematical Society
First Published:First published in Transactions of the American Mathematical Society 372(3): 1985-2010
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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