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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Abstract
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 |
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Additional Information: | The first named author was supported by EPSRC grant EP/M009718/1. |
Status: | Published |
Refereed: | Yes |
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: | 0002-9947 |
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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