Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Cartan subalgebras in C*-algebras. Existence and uniqueness


Authors: Xin Li and Jean Renault
Journal: Trans. Amer. Math. Soc. 372 (2019), 1985-2010
MSC (2010): Primary 46L05, 22A22; Secondary 46L85
DOI: https://doi.org/10.1090/tran/7654
Published electronically: April 12, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 46L05, 22A22, 46L85

Retrieve articles in all journals with MSC (2010): 46L05, 22A22, 46L85


Additional Information

Xin Li
Affiliation: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
Email: xin.li@qmul.ac.uk

Jean Renault
Affiliation: Université d’Orléans et CNRS (UMR 7349 et FR2964), Département de Mathématiques, F-45067 Orléans Cedex 2, France
Email: jean.renault@univ-orleans.fr

DOI: https://doi.org/10.1090/tran/7654
Received by editor(s): November 25, 2017
Received by editor(s) in revised form: June 25, 2018, and June 28, 2018
Published electronically: April 12, 2019
Additional Notes: The first named author was supported by EPSRC grant EP/M009718/1.
Article copyright: © Copyright 2019 American Mathematical Society