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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2019

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

Xin Li
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Jean N Renault
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Résumé

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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Dates et versions

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

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  • HAL Id : hal-03117017 , version 1

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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⟩
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