Rokhlin dimension for actions of residually compact groups

Fuente: arXiv
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Main Authors: Cao, Xin, Fang, Xiaochun, Wu, Jianchao
Format: Preprint
Published: 2026
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author Cao, Xin
Fang, Xiaochun
Wu, Jianchao
author_facet Cao, Xin
Fang, Xiaochun
Wu, Jianchao
contents We introduce the concept of Rokhlin dimension for actions of residually compact groups on C*-algebras, which extends and unifies previous notions for actions of compact groups, residually finite groups and the reals. We then demonstrate that finite nuclear dimension (respectively, absorption of a strongly self-absorbing C*-algebra) is preserved under the formation of crossed products by residually compact group actions with finite Rokhlin dimension (respectively, finite Rokhlin dimension with commuting towers). Furthermore, if second countable residually compact group contains a non-open cocompact closed subgroup, then crossed products arising from actions with finite Rokhlin dimension are stable. Finally, we study the relationship between the tube dimension of a topological dynamical system and the Rokhlin dimension of the induced C*-dynamical system.
format Preprint
id arxiv_https___arxiv_org_abs_2601_15694
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Rokhlin dimension for actions of residually compact groups
Cao, Xin
Fang, Xiaochun
Wu, Jianchao
Operator Algebras
46L55
We introduce the concept of Rokhlin dimension for actions of residually compact groups on C*-algebras, which extends and unifies previous notions for actions of compact groups, residually finite groups and the reals. We then demonstrate that finite nuclear dimension (respectively, absorption of a strongly self-absorbing C*-algebra) is preserved under the formation of crossed products by residually compact group actions with finite Rokhlin dimension (respectively, finite Rokhlin dimension with commuting towers). Furthermore, if second countable residually compact group contains a non-open cocompact closed subgroup, then crossed products arising from actions with finite Rokhlin dimension are stable. Finally, we study the relationship between the tube dimension of a topological dynamical system and the Rokhlin dimension of the induced C*-dynamical system.
title Rokhlin dimension for actions of residually compact groups
topic Operator Algebras
46L55
url https://arxiv.org/abs/2601.15694