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Simplicity of reduced crossed products
Abstract
We characterize the simplicity of reduced crossed product C*-algebras in terms of stabilizer subgroups. Specifically, we prove that if G is a countable group and X is a minimal G-flow, then the reduced crossed product C*-algebra C(X) ×λG is simple if and only if there is a point in X with a C*-simple stabilizer subgroup. Further, these conditions are equivalent to a generic point in X having a C*-simple stabilizer subgroup. We also provide an example demonstrating that this result does not extend to uncountable groups. This completely resolves a question of Ozawa.
Related
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- Selfless Reduced Crossed Product C*-Algebras Arising from Almost Periodic Actions
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- Isomorphisms of ℓ1-crossed products of topological systems
- KS-Groupoids and KS-Crossed Products associated with Inverse Semigroup Actions
BibTeX
@misc{bray2026simplicity,
title = {{Simplicity of reduced crossed products}},
author = {Thomas Bray and Matthew Kennedy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.17025},
eprint = {2608.17025},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17025},
}
RIS
TY - UNPB
TI - Simplicity of reduced crossed products
AU - Thomas Bray
AU - Matthew Kennedy
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2608.17025
UR - https://arxiv.org/abs/2608.17025
AB - We characterize the simplicity of reduced crossed product C*-algebras in terms of stabilizer subgroups. Specifically, we prove that if G is a countable group and X is a minimal G-flow, then the reduced crossed product C*-algebra C(X) ×_λG is simple if and only if there is a point in X with a C*-simple stabilizer subgroup. Further, these conditions are equivalent to a generic point in X having a C*-simple stabilizer subgroup. We also provide an example demonstrating that this result does not extend to uncountable groups. This completely resolves a question of Ozawa.
ER -