C*-irreducibility for reduced twisted group C*-algebras

Bédos, Erik; Omland, Tron

doi:10.48550/arxiv.2203.16998

Cited by 1 publication

(4 citation statements)

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“…discrete groups Γ by Cameron-Smith, [4], again assuming Γ A is outer, Λ is the trivial group, and A is simple. This was further extended by Bedos and Omland, [2,Theorem 5.3], to the general case of (ii) below, assuming that the (twisted) action of Γ/Λ on A is outer, in which case they can deduce their result from the Cameron-Smith theorem. Our proof below is self-contained, and uses normality of Λ in Γ in a different way.…”

Section: Theorem 34 Let γmentioning

confidence: 90%

“…[19], i.e., all intermediate C * -algebras are simple. This is a classical result when Λ is the trivial group, see [19], and was extended to normal subgroups Λ ✁ Γ in [2].…”

Section: Introductionmentioning

confidence: 88%

“…Our proof below is self-contained, and uses normality of Λ in Γ in a different way. Part (i) also follows from [2,Theorem 5.3] in the case of Λ being normal in Γ, but we exend their result to cover the general, not necessarily normal, case.…”

Section: Theorem 34 Let γmentioning

confidence: 97%

“…This result is already known (even for outer actions), cf. Cameron-Smith, [4] (when Λ is trivial) and Bedos-Omland, [2], using [4]. We give here an elementary self-contained proof using the strong averaging property.…”

Section: Introductionmentioning

confidence: 99%

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A Dixmier type averaging property of automorphisms on a $C^*$-algebra

Rørdam¹

2022

Preprint

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In his study of the relative Dixmier property for inclusions of von Neumann algebras and of C * -algebras, Popa considered a certain property of automorphisms on C * -algebras, that we here call the strong averaging property. In this note we characterize when an automorphism on a C * -algebra has the strong averaging property. In particular, automophisms on commutative C * -algebras possess this property precisely when they are free. An automorphism on a unital separable simple C * -algebra with at least one tracial state has the strong averaging property precisely when its extension to the finite part of the bi-dual of the C * -algebra is properly outer, and in the simple, non-tracial case the strong averaging property is equivalent to being outer.To illustrate the usefulness of the strong averaging property we give three examples where we can provide simpler proofs of existing results on crossed product C * -algebras, and we are also able to extend these results in different directions.

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Section: Theorem 34 Let γmentioning

confidence: 90%

“…[19], i.e., all intermediate C * -algebras are simple. This is a classical result when Λ is the trivial group, see [19], and was extended to normal subgroups Λ ✁ Γ in [2].…”

Section: Introductionmentioning

confidence: 88%

Section: Theorem 34 Let γmentioning

confidence: 97%