Rokhlin Dimension: Permanence Properties and Ideal Separation
Operator Algebras
2024-05-28 v2 Functional Analysis
Abstract
We study the Rokhlin dimension for actions of residually finite groups on C*-algebras. We give a definition equivalent to the original one due to Szabo, Wu and Zacharias. We then prove a number of permanence properties and discuss actions on C_0(X)-algebras and commutative C*- algebras. Finally, we use a theorem of Sierakowski to show that, for an action with finite Rokhlin dimension, every ideal in the associated reduced crossed product C*-algebra arises from an invariant ideal of the underlying algebra.
Keywords
Cite
@article{arxiv.2305.06675,
title = {Rokhlin Dimension: Permanence Properties and Ideal Separation},
author = {Sureshkumar M and Prahlad Vaidyanathan},
journal= {arXiv preprint arXiv:2305.06675},
year = {2024}
}
Comments
Accepted in Groups, Geometry, and Dynamics. Few small corrections made