Cartan subalgebras in C*-algebras. Existence and uniqueness
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- by Xin Li and Jean Renault PDF
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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.References
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Additional Information
- Xin Li
- Affiliation: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
- MR Author ID: 911893
- ORCID: 0000-0002-2243-3742
- 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
- MR Author ID: 146950
- Email: jean.renault@univ-orleans.fr
- 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.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 1985-2010
- MSC (2010): Primary 46L05, 22A22; Secondary 46L85
- DOI: https://doi.org/10.1090/tran/7654
- MathSciNet review: 3976582