## Advanced Studies in Pure Mathematics

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

Yasuhiko Sato

#### 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.

#### Article information

Dates
Revised: 28 February 2017
First available in Project Euclid: 21 August 2019

Sato, Yasuhiko. Actions of amenable groups and crossed products of $\mathcal{Z}$-absorbing $\mathrm{C}^*$-algebras. Operator Algebras and Mathematical Physics, 189--210, Mathematical Society of Japan, Tokyo, Japan, 2019. doi:10.2969/aspm/08010189. https://projecteuclid.org/euclid.aspm/1566404316