Equivariant property Gamma and the tracial local-to-global principle for C*-dynamics

Autor:	Szabó, Gábor, Wouters, Lise
Rok vydání:	2023
Předmět:	Mathematics - Operator Algebras 46L55
Druh dokumentu:	Working Paper
Popis:	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. Comment: 47 pages, various small corrections and added details. This version has been accepted for publication by APDE
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.12846 Zobrazit plný text záznamu View this record from Arxiv