Rokhlin dimension for actions of residually finite groups

DOI10.1017/etds.2017.113zbMath1451.37014arXiv1408.6096OpenAlexW2964340885MaRDI QIDQ4968758

Jianchao Wu, Gábor Szabó, Joachim Zacharias

Publication date: 9 July 2019

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.6096

zbMATH Keywords

residually finite groupsRokhlin dimension$\text{C}^{\ast}$-algebra

Mathematics Subject Classification ID

Dimension theory in general topology (54F45) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) General groups of measure-preserving transformations and dynamical systems (37A15) Dimension theory of smooth dynamical systems (37C45) Measurable group actions (22F10) Dynamical systems and the theory of (C^*)-algebras (37A55)

Related Items (27)

The type semigroup, comparison, and almost finiteness for ample groupoids ⋮ Strongly outer actions of amenable groups on \(\mathcal{Z}\)-stable nuclear \(C^\ast\)-algebras ⋮ Polynomial growth, comparison, and the small boundary property ⋮ Nuclear dimension of simple \(\mathrm{C}^*\)-algebras ⋮ 𝐶*-algebras and their nuclear dimension ⋮ Equivariant \({\mathcal{Z}} \)-stability for single automorphisms on simple \(C^*\)-algebras with tractable trace simplices ⋮ Rokhlin-type properties of group actions on operator algebras ⋮ Chaotic tracial dynamics ⋮ Exotic circle actions on classifiable \(C^\ast\)-algebras ⋮ Dynamical comparison and \(\mathcal{Z} \)-stability for crossed products of simple \(C^\ast \)-algebras ⋮ Rokhlin dimension: absorption of model actions ⋮ Dimension, comparison, and almost finiteness ⋮ On $C^*$-algebras associated to actions of discrete subgroups of $\operatorname{SL}(2,\mathbb{R})$ on the punctured plane ⋮ On a categorical framework for classifying \(C^\ast\)-dynamics up to cocycle conjugacy ⋮ Sofic boundaries of groups and coarse geometry of sofic approximations ⋮ Group actions on Smale space -algebras ⋮ Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and \(C^\ast\)-algebras ⋮ Følner tilings for actions of amenable groups ⋮ Rokhlin dimension for flows ⋮ Nuclear dimension of crossed products associated to partial dynamical systems ⋮ The nuclear dimension of \(C^\ast \)-algebras associated to topological flows and orientable line foliations ⋮ Groupoid models of \(C^*\)-algebras and the Gelfand functor ⋮ Almost finiteness and the small boundary property ⋮ Rokhlin dimension of ℤm-actions on simple C∗-algebras ⋮ Dynamic asymptotic dimension for actions of virtually cyclic groups ⋮ Partial C*-dynamics and Rokhlin dimension ⋮ Conditional mean dimension

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Rokhlin type theorem for simple \(C^{\ast}\)-algebras of finite nuclear dimension
• Rokhlin dimension: obstructions and permanence properties
• The nuclear dimension of \(C^\ast\)-algebras associated to homeomorphisms
• Minimal dynamics and \(K\)-theoretic rigidity: Elliott's conjecture
• Box spaces, group extensions and coarse embeddings into Hilbert space
• \(\mathcal{Z}\)-stability of crossed products by strongly outer actions
• Central sequence \(C^*\)-algebras and tensorial absorption of the Jiang-Su algebra
• Decomposition rank of UHF-absorbing \(C^\ast\)-algebras
• Quasidiagonality of nuclear \(\mathrm{C}^\ast\)-algebras
• Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and \(C^\ast\)-algebras
• Rokhlin dimension for flows
• Crossed products by finite group actions with the Rokhlin property
• Nuclear dimension and \(\mathcal{Z}\)-stability of pure \(C^{\ast}\)-algebras
• Crossed products by compact group actions with the Rokhlin property
• Finite group actions on \(C^*\)-algebras with the Rohlin property. I
• Strict comparison and \(\mathcal{Z}\)-absorption of nuclear \(C^*\)-algebras
• Large scale geometry
• Properties of topological dynamical systems and corresponding \(C^*\)- algebras
• Nuclear dimension and \(\mathcal Z\)-stability
• Equivariant covers for hyperbolic groups.
• Rokhlin actions and self-absorbing \(C^\ast\)-algebras
• \(\mathbb Z^2\)-actions on Kirchberg algebras
• The Rohlin property for automorphisms of the Jiang-Su algebra
• Group and ring theoretic properties of polycyclic groups.
• Stability for integer actions on UHF \(C^*\)-algebras
• Unbounded derivations in AT algebras
• The Rohlin property for \(\mathbb{Z}^2\)-actions on UHF algebras
• The Baum-Connes conjecture for amenable foliations
• Lifting solutions to perturbing problems in \(C^*\)-algebras
• Equivariant Kirchberg-Phillips-type absorption for amenable group actions
• The asymptotic dimension of box spaces of virtually nilpotent groups
• Finite group actions on \(C^{*}\)-algebras with the Rohlin property. II
• Period two automorphisms of UHF C*-algebras
• Lowering topological entropy
• A Rohlin property for one-parameter automorphism groups
• The Rohlin property for shifts on UHF algebras and automorphisms of Cuntz algebras
• Rokhlin dimension and \(C^\ast\)-dynamics
• Rohlin flows on the Cuntz algebra \(\mathcal O_\infty\)
• Localizing the Elliott conjecture at strongly self-absorbing \(C^*\)-algebras
• Decomposition rank of \(\mathcal{Z}\)-stable \(C^*\)-algebras
• Decomposition rank and \(\mathcal{Z}\)-stability
• Ƶ-Stability of Crossed Products by Strongly Outer Actions II
• Nuclear dimension and 𝒵-stability of non-simple 𝒞*-algebras
• Coarse flow spaces for relatively hyperbolic groups
• The tracial Rokhlin property for actions of finite groups on C*-algebras
• Classifying crossed product C*-algebras
• Generalized Bunce–Deddens algebras
• Strongly self-absorbing $C^{*}$-algebras
• Mean dimension and Jaworski-type theorems
• Completely positive maps of order zero
• Twisted crossed products of C*-algebras
• Outer conjugacy classes of automorphisms of factors
• Regularity properties and Rokhlin dimension for compact group actions
• Geometric Group Theory
• ROHLIN FLOWS ON THE CUNTZ ALGEBRA ${\mathcal O}_2$
• The Rohlin property for automorphisms of UHF algebras
• Rokhlin dimension of ℤm-actions on simple C∗-algebras
• The Rokhlin dimension of topological ℤ^m -actions
• Z-Stability and Finite-Dimensional Tracial Boundaries
• Crossed products by actions of finite groups with the Rokhlin property
• Rokhlin dimension for compact group actions
• Covering dimension for nuclear 𝐶*-algebras II
• Covering Dimension of C*-Algebras and 2-Coloured Classification
• Shorter Notes: Representations of Polycyclic Groups
• Representations of Twisted Group Algebras
• The Group Ring Of a Class Of Infinite Nilpotent Groups
• Classification of nuclear \(C^*\)-algebras. Entropy in operator algebras
• The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras

This page was built for publication: Rokhlin dimension for actions of residually finite groups