MINIMAL DYNAMICS AND $\mathcal{Z}$-STABLE CLASSIFICATION

DOI10.1142/S0129167X10006665zbMath1218.46037arXiv1001.1268OpenAlexW2164542532MaRDI QIDQ3081478

Karen R. Strung, Wilhelm Winter

Publication date: 8 March 2011

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1268

zbMATH Keywords

classificationJiang-Su algebratracial approximationminimal homeomorphisms\(\mathcal Z\)-stabilityordered \(K\)-groupsuniquely ergodic minimal dynamical systems

Mathematics Subject Classification ID

Noncommutative topology (46L85) Noncommutative dynamical systems (46L55) Classifications of (C^*)-algebras (46L35)

Related Items (10)

Polynomial growth, comparison, and the small boundary property ⋮ Minimal dynamics and \(K\)-theoretic rigidity: Elliott's conjecture ⋮ Bipolar theorem for quantum cones ⋮ Constructing minimal homeomorphisms on point-like spaces and a dynamical presentation of the Jiang-Su algebra ⋮ Groups and dynamics: topology, measure, and Borel structure. Abstracts from the workshop held January 16--22, 2022 ⋮ Crossed products of C∗-algebras C(X,A) and their applications ⋮ \(C^\ast\)-algebras of minimal dynamical systems of the product of a Cantor set and an odd dimensional sphere ⋮ Decomposition rank of approximately subhomogeneous \(C^*\)-algebras ⋮ The Rokhlin dimension of topological ℤ^m -actions ⋮ UHF-slicing and classification of nuclear C*-algebras

Cites Work

• Simple \(C^{*}\)-algebras with locally finite decomposition rank
• Lifting \(KK\)-elements, asymptotic unitary equivalence and classification of simple C\(^*\)-algebras
• Comparison theory and smooth minimal \(C^*\)-dynamics
• The \(C^*\)-algebras associated with minimal homeomorphisms of the Cantor set
• An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R
• On the structure of simple \(C^*\)-algebras tensored with a UHF-algebra
• On the structure of simple \(C^*\)-algebras tensored with a UHF-algebra. II
• Approximately central matrix units and the structure of noncommutative tori
• Stable isomorphism of hereditary subalgebras of \(C^*\)-algebras
• Simple \(C^*\)-algebras generated by isometries
• The structure of the irrational rotation \(C^*\)-algebra
• Simple nuclear \(C^{*}\)-algebras of tracial topological rank one
• On tracial approximation
• Decomposition rank and \(\mathcal{Z}\)-stability
• The Tracial Topological Rank of C*-Algebras
• Minimal dynamics and the classification of C*-algebras
• Tracially AF 𝐶*-algebras
• Cancellation and stable rank for direct limits of recursive subhomogeneous algebras

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