Equivariant property Gamma and the tracial local-to-global principle for C*-dynamics
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915321887064064 |
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| author | Szabó, Gábor Wouters, Lise |
| author_facet | Szabó, Gábor Wouters, Lise |
| contents | We consider the notion of equivariant uniform property Gamma for actions of countable discrete groups on C*-algebras that admit traces. In case the group is amenable and the C*-algebra has a compact tracial state space, we prove that this property implies a kind of tracial local-to-global principle for the C*-dynamical system, generalizing a recent such principle for C*-algebras exhibited in work of Castillejos et al. For actions on simple nuclear $\mathcal{Z}$-stable C*-algebras, we use this to prove that equivariant uniform property Gamma is equivalent to equivariant $\mathcal{Z}$-stability, generalizing a result of Gardella-Hirshberg-Vaccaro. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2301_12846 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equivariant property Gamma and the tracial local-to-global principle for C*-dynamics Szabó, Gábor Wouters, Lise Operator Algebras 46L55 We consider the notion of equivariant uniform property Gamma for actions of countable discrete groups on C*-algebras that admit traces. In case the group is amenable and the C*-algebra has a compact tracial state space, we prove that this property implies a kind of tracial local-to-global principle for the C*-dynamical system, generalizing a recent such principle for C*-algebras exhibited in work of Castillejos et al. For actions on simple nuclear $\mathcal{Z}$-stable C*-algebras, we use this to prove that equivariant uniform property Gamma is equivalent to equivariant $\mathcal{Z}$-stability, generalizing a result of Gardella-Hirshberg-Vaccaro. |
| title | Equivariant property Gamma and the tracial local-to-global principle for C*-dynamics |
| topic | Operator Algebras 46L55 |
| url | https://arxiv.org/abs/2301.12846 |