Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Cartan subalgebras in C*-algebras. Existence and uniqueness
HTML articles powered by AMS MathViewer

by Xin Li and Jean Renault PDF
Trans. Amer. Math. Soc. 372 (2019), 1985-2010 Request permission

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
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
  • 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