Asymptotic unitary equivalence and classification of simple amenable \(C^{\ast}\)-algebras

DOI10.1007/s00222-010-0280-9zbMath1255.46031OpenAlexW2052585099MaRDI QIDQ633100

Huaxin Lin

Publication date: 31 March 2011

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00222-010-0280-9

zbMATH Keywords

classificationtracial rankseparable amenable simple \(C^{\ast}\)-algebrasUniversal Coefficient Theorem

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Classifications of (C^*)-algebras (46L35)

Related Items

Tensor products of classifiable C∗-algebras ⋮ The tracial topological rank of extensions of \(C^*\)-algebras ⋮ Approximated by finite-dimensional homomorphisms into simple $C^*$-algebras with tracial rank one ⋮ Crossed products and minimal dynamical systems ⋮ Constructing minimal homeomorphisms on point-like spaces and a dynamical presentation of the Jiang-Su algebra ⋮ 𝐶*-algebras and their nuclear dimension ⋮ Tracial approximation in simple -algebras ⋮ Asymptotic unitary equivalence in \(C^\ast\)-algebras ⋮ Note on compact operators on a Hilbert \(C^\ast\)-module ⋮ Homomorphisms into simple \(\mathcal{Z}\)-stable \(C^*\)-algebras. II ⋮ A classification of inductive limit C∗$C^{*}$‐algebras with ideal property ⋮ Abstract classification theorems for amenable \(C^\ast\)-algebras ⋮ Homomorphisms from AH-algebras ⋮ Classification of extensions of torus algebra. II ⋮ Tracial oscillation zero and \(\mathcal{Z}\)-stability ⋮ The corona algebra of the stabilized Jiang-Su algebra ⋮ Crossed product \(C^\ast\)-algebras of minimal dynamical systems on the product of the Cantor set and the torus ⋮ Regularity for stably projectionless, simple \(C^\ast\)-algebras ⋮ Exponentials in simple \(\mathcal Z\)-stable \(C^\ast\)-algebras ⋮ Nuclear dimension and \(\mathcal{Z}\)-stability of pure \(C^{\ast}\)-algebras ⋮ CROSSED PRODUCTS OF CERTAIN C*-ALGEBRAS ⋮ The classification of simple separable unital \(\mathcal{Z}\)-stable locally ASH algebras ⋮ Mean dimension and AH-algebras with diagonal maps ⋮ \(C^\ast\)-algebras of minimal dynamical systems of the product of a Cantor set and an odd dimensional sphere ⋮ Kishimoto's conjugacy theorems in simple \(C^\ast\)-algebras of tracial rank one ⋮ Continuity of functors with respect to generalized inductive limits ⋮ \(C^*\) exponential length of commutators unitaries in AH-algebras ⋮ Decomposition rank of approximately subhomogeneous \(C^*\)-algebras ⋮ The automorphism group of a simple $\mathcal {Z}$-stable $C^{*}$-algebra ⋮ On locally AH algebras ⋮ Unital extensions of AF-algebras by purely infinite simple algebras ⋮ On the nuclear dimension of certain UCT-Kirchberg algebras ⋮ UHF-slicing and classification of nuclear C*-algebras ⋮ Tracial approximation is stable

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the classification of \(C^*\)-algebras of real rank zero. II
• The soft torus and applications to almost commuting matrices
• Produits finis de commutateurs dans les \(C^*\)-algèbres
• On the classification of simple inductive limit \(C^{*}\)-algebras. II: The isomorphism theorem
• Lifting \(KK\)-elements, asymptotic unitary equivalence and classification of simple C\(^*\)-algebras
• The Elliott conjecture for Villadsen algebras of the first type
• The range of approximate unitary equivalence classes of homomorphisms from AH-algebras
• AF embeddings of \(C(\mathbb{T}^ 2)\) with a prescribed \(K\)-theory
• Extending states on preordered semigroups and the existence of quasitraces on \(C^ \ast\)-algebras
• Classification of simple \(C^{\ast}\)-algebras and higher dimensional noncommutative tori
• Embedding an AH-algebra into a simple \(C^*\)-algebra with prescribed \(KK\)-data
• Classification of simple \(C^*\)-algebras of tracial topological rank zero
• \(C^*\)-algebra homomorphisms and \(KK\)-theory
• On the classification of simple inductive limit \(C^*\)-algebras. I: The reduction theorem
• Classification of certain infinite simple \(C^*\)-algebras. II
• Limits of circle algebras
• Traces, unitary characters and crossed products by \(\mathbb{Z}\)
• A universal multicoefficient theorem for the Kasparov groups
• Homotopy of unitaries in simple \(C^{*}\)-algebras with tracial rank one
• Simple nuclear \(C^{*}\)-algebras of tracial topological rank one
• Localizing the Elliott conjecture at strongly self-absorbing \(C^*\)-algebras
• Localizing the Elliott conjecture at strongly self-absorbing \(C^*\)-algebras. II
• On some \(C^ *\)-algebras considered by Glimm
• The Tracial Topological Rank of C*-Algebras
• On the classification of C*-algebras of real rank zero.
• Unitary equivalences for essential extensions of $C^*$-algebras
• Strongly self-absorbing $C^{*}$-algebras
• AF-embedding of crossed products of AH-algebras by $\mathbb{Z}$ and asymptotic AF-embedding
• AF-Embeddings of the Crossed Products of AH-Algebras by Finitely Generated Abelian Groups
• Asymptotically unitary equivalence and asymptotically inner automorphisms
• K-Theory and Asymptotically Commuting Matrices
• On a Simple Unital Projectionless C*-Algebra
• Classification of Certain SimpleC*-Algebras with Torsion inK₁
• Simple 𝐴𝐻-algebras of real rank zero
• Injectivity of the Connecting Maps in AH Inductive Limit Systems
• Approximate unitary equivalence in simple $C^{*}$-algebras of tracial rank one