Actions of amenable groups and crossed products of $\mathcal{Z}$-absorbing $\mathrm{C}^*$-algebras

Sato, Yasuhiko

doi:10.2969/aspm/08010189

VOL. 80 | 2019 Actions of amenable groups and crossed products of $\mathcal{Z}$-absorbing $\mathrm{C}^*$-algebras

Yasuhiko Sato

Editor(s) Masaki Izumi, Yasuyuki Kawahigashi, Motoko Kotani, Hiroki Matui, Narutaka Ozawa

Adv. Stud. Pure Math., 2019: 189-210 (2019) DOI: 10.2969/aspm/08010189

Abstract

We study actions of countable discrete amenable groups on unital separable simple nuclear $\mathcal{Z}$-absorbing $\mathrm{C}^*$-algebras. Under a certain assumption on tracial states, which is automatically satisfied in the case of a unique tracial state, the crossed product is shown to absorb the Jiang-Su algebra $\mathcal{Z}$ tensorially.