Ergodic automorphisms on Kirchberg algebras
Operator Algebras
2025-05-30 v1
Abstract
Combining the theory of extensions of C*-algebras and the Pimsner construction, we show that every countable infinite discrete group admits an ergodic action on arbitrary unital Kirchberg algebra. In the proof, we give a Pimsner construction realizing many unital subalgebras of a given unital Kirchberg algebra as the fixed point algebras of single automorphisms. Furthermore, for amenable infinite discrete groups, we show that every point-wise outer action on arbitrary unital Kirchberg algebra has an ergodic cocycle perturbation with the help of Gabe--Szab\'{o}'s theorem and Baum--Connes' conjecture.
Cite
@article{arxiv.2505.23168,
title = {Ergodic automorphisms on Kirchberg algebras},
author = {Kengo Matsumoto and Taro Sogabe},
journal= {arXiv preprint arXiv:2505.23168},
year = {2025}
}