PreprintCC BY 4.0arXiv
Selfless nonnuclear crossed products
Abstract
For a strictly ergodic action of a countable discrete group with Ozawa's property PHP on the Cantor set, we prove that dynamical comparison implies complete selflessness of its reduced crossed product. Therefore these crossed products have stable rank one, strict comparison, a unique quasitracial state, and real rank zero. Applications include probability-measure-preserving Cantor actions of C*-simple acylindrically hyperbolic and C*-simple linear groups for which an infinite amenable subgroup acts strictly ergodically. The results also apply to subodometers and infinite regular Toeplitz subshifts of residually finite groups with PHP.
Related
- Selfless Reduced Crossed Product C*-Algebras Arising from Almost Periodic Actions
- Selfless reduced free products and graph products of C⁎-algebras
- Simplicity of reduced crossed products
- Isomorphisms of ℓ1-crossed products of topological systems
- KS-Groupoids and KS-Crossed Products associated with Inverse Semigroup Actions
BibTeX
@misc{bell2026selfless,
title = {{Selfless nonnuclear crossed products}},
author = {Jamie Bell},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.34011},
eprint = {2609.34011},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34011},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Selfless nonnuclear crossed products
AU - Jamie Bell
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2609.34011
UR - https://arxiv.org/abs/2609.34011
AB - For a strictly ergodic action of a countable discrete group with Ozawa's property PHP on the Cantor set, we prove that dynamical comparison implies complete selflessness of its reduced crossed product. Therefore these crossed products have stable rank one, strict comparison, a unique quasitracial state, and real rank zero. Applications include probability-measure-preserving Cantor actions of C*-simple acylindrically hyperbolic and C*-simple linear groups for which an infinite amenable subgroup acts strictly ergodically. The results also apply to subodometers and infinite regular Toeplitz subshifts of residually finite groups with PHP.
ER -