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

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.
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https://hal.archives-ouvertes.fr/hal-03117017
Contributor : Jean Renault Connect in order to contact the contributor
Submitted on : Wednesday, January 20, 2021 - 5:57:36 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM
Long-term archiving on: : Wednesday, April 21, 2021 - 7:07:52 PM

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  • HAL Id : hal-03117017, version 1

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

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