Cartan subalgebras in C*-algebras. Existence and uniqueness. - Archive ouverte HAL Access content directly
Journal Articles Transactions of the American Mathematical Society Year : 2019

Cartan subalgebras in C*-algebras. Existence and uniqueness.

(1) , (2)
1
2
Xin Li
  • Function : Author
  • PersonId : 1089166
Jean N Renault
  • Function : Author
  • PersonId : 965102

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 analysed systematically using the theory of fibre 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 Roe algebras.
Fichier principal
Vignette du fichier
1703.10505.pdf (350.02 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03117017 , version 1 (20-01-2021)

Identifiers

  • HAL Id : hal-03117017 , version 1

Cite

Xin Li, Jean N Renault. Cartan subalgebras in C*-algebras. Existence and uniqueness.. Transactions of the American Mathematical Society, 2019, 372 (3), pp.1985-2010. ⟨hal-03117017⟩
46 View
96 Download

Share

Gmail Facebook Twitter LinkedIn More