Advanced Studies in Pure Mathematics

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

Yasuhiko Sato

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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

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

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

Permanent link to this document euclid.aspm/1566404316

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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