Advanced Studies in Pure Mathematics

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

Yasuhiko Sato

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Source
Operator Algebras and Mathematical Physics, M. Izumi, Y. Kawahigashi, M. Kotani, H. Matui and N. Ozawa, eds. (Tokyo: Mathematical Society of Japan, 2019), 189-210

Dates
Received: 27 December 2016
Revised: 28 February 2017
First available in Project Euclid: 21 August 2019

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1566404316

Digital Object Identifier
doi:10.2969/aspm/08010189

Zentralblatt MATH identifier
07116429

Subjects
Primary: 46L06: Tensor products of $C^*$-algebras 46L35: Classifications of $C^*$-algebras 46L40: Automorphisms 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

Citation

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


Export citation