Minimal dynamics and the classification of C*-algebras

DOI10.1073/pnas.0903629106zbMath1203.46046OpenAlexW2108315492WikidataQ37386118 ScholiaQ37386118MaRDI QIDQ3069229

Andrew S. Toms, Wilhelm Winter

Publication date: 24 January 2011

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.0903629106

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) General theory of (C^*)-algebras (46L05) Classifications of (C^*)-algebras (46L35) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (27)

Topologically conjugate classifications of the translation actions on low-dimensional compact connected Lie groups ⋮ Crossed products and minimal dynamical systems ⋮ Constructing minimal homeomorphisms on point-like spaces and a dynamical presentation of the Jiang-Su algebra ⋮ Nuclear dimension and \(\mathcal Z\)-stability ⋮ Perturbations of nuclear \(C^*\)-algebras ⋮ Classifiable \(\mathrm{C}^*\)-algebras from minimal \(\mathbb{Z} \)-actions and their orbit-breaking subalgebras ⋮ K-theoretic rigidity and slow dimension growth ⋮ Classifiability of crossed products by nonamenable groups ⋮ Nuclear dimension and classification of 𝐶*-algebras associated to Smale spaces ⋮ Some classifiable groupoid \(C^{*}\)-algebras with prescribed \(K\)-theory ⋮ On $C^*$-algebras associated to actions of discrete subgroups of $\operatorname{SL}(2,\mathbb{R})$ on the punctured plane ⋮ Dynamical classification for complex matrices ⋮ Nuclear dimension and \(\mathcal{Z}\)-stability of pure \(C^{\ast}\)-algebras ⋮ Group actions on Smale space -algebras ⋮ CROSSED PRODUCTS OF CERTAIN C*-ALGEBRAS ⋮ The classification of simple separable unital \(\mathcal{Z}\)-stable locally ASH algebras ⋮ Rokhlin dimension for flows ⋮ The nuclear dimension of \(C^{*}\)-algebras ⋮ Nuclear dimension of crossed products associated to partial dynamical systems ⋮ \(C^\ast\)-algebras of minimal dynamical systems of the product of a Cantor set and an odd dimensional sphere ⋮ The spatial isomorphism problem for close separable nuclear C*-algebras ⋮ MINIMAL DYNAMICS AND $\mathcal{Z}$-STABLE CLASSIFICATION ⋮ THE CUNTZ SEMIGROUP OF CONTINUOUS FUNCTIONS INTO CERTAIN SIMPLE C*-ALGEBRAS ⋮ Decomposition rank of approximately subhomogeneous \(C^*\)-algebras ⋮ On locally AH algebras ⋮ Local trivializations of suspended minimal Cantor systems and the stable orbit-breaking subalgebra ⋮ UHF-slicing and classification of nuclear C*-algebras

Cites Work

• Lifting \(KK\)-elements, asymptotic unitary equivalence and classification of simple C\(^*\)-algebras
• An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R
• The structure of the irrational rotation \(C^*\)-algebra
• Regularity properties in the classification program for separable amenable C*-algebras
• Orbit equivalence for Cantor minimal ℤ²-systems
• COVERING DIMENSION AND QUASIDIAGONALITY
• Recursive subhomogeneous algebras
• ON THE CLASSIFICATION OF SIMPLE ${{\mathcal Z}}$-STABLE $C^{*}$-ALGEBRAS WITH REAL RANK ZERO AND FINITE DECOMPOSITION RANK

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