Tracially amenable actions and purely infinite crossed products
Journal article, 2024

We introduce the notion of tracial amenability for actions of discrete groups on unital, tracial C∗-algebras, as a weakening of amenability where all the relevant approximations are done in the uniform trace norm. We characterize tracial amenability with various equivalent conditions, including topological amenability of the induced action on the trace space. Our main result concerns the structure of crossed products: for groups containing the free group F2, we show that outer, tracially amenable actions on simple, unital, Z-stable C∗-algebras always have purely infinite crossed products. Finally, we give concrete examples of tracially amenable actions of free groups on simple, unital AF-algebras.

Author

Eusebio Gardella

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Shirly Geffen

University of Münster

Julian Kranz

University of Münster

Petr Naryshkin

University of Münster

Andrea Vaccaro

University of Münster

Mathematische Annalen

0025-5831 (ISSN) 1432-1807 (eISSN)

Vol. 390 3 3665-3690

Subject Categories

Algebra and Logic

DOI

10.1007/s00208-024-02833-9

More information

Latest update

10/12/2024