Actions on classifiable C*-algebras without equivariant property (SI)
Journal article, 2024

We exhibit examples of actions of countable discrete groups on both simple and non-simple nuclear stably finite C*-algebras that are tracially amenable but not amenable. We furthermore obtain that, under the additional assumption of strict comparison, amenability is equivalent to tracial amenability plus the equivariant analogue of Matui–Sato's property (SI). By virtue of this equivalence, our construction yields the first known examples of actions on classifiable C*-algebras that do not have equivariant a over show that such actions can be chosen to absorb the trivial action on the universal UHF algebra, thus proving that equivariant (Formula presented.) -stability does not in general imply equivariant property (SI).

Author

Eusebio Gardella

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Julian Kranz

Prof. Dr. Fabian Gieseke

Andrea Vaccaro

University of Münster

Bulletin of the London Mathematical Society

0024-6093 (ISSN) 1469-2120 (eISSN)

Vol. 56 12 3623-3633

Subject Categories

Subatomic Physics

Discrete Mathematics

DOI

10.1112/blms.13154

More information

Latest update

12/16/2024