On the classification of \(C^*\)-algebras of real rank zero. II
From MaRDI portal
Publication:674542
DOI10.2307/2118565zbMath0867.46041OpenAlexW1986808251MaRDI QIDQ674542
George A. Elliott, Guihua Gong
Publication date: 10 August 1997
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2118565
classificationinductive limitpositive coneRiesz decomposition propertyreal rank zerofinite direct sums of homogeneous \(C^*\)-algebrasgraded dimension rangeselfadjoint elementsseparable nuclear simple \(C^*\)-algebrasspectrum 3-dimensional finite CW complexesstable rank one
(K)-theory and operator algebras (including cyclic theory) (46L80) Inductive and projective limits in functional analysis (46M40) Classifications of (C^*)-algebras (46L35)
Related Items (only showing first 100 items - show all)
Tensor products of classifiable C∗-algebras ⋮ Morita equivalence for quantum Heisenberg manifolds ⋮ Toms-Winter conjecture for \(C^\ast\)-modules ⋮ A classification of inductive limit C∗$C^{*}$‐algebras with ideal property ⋮ Symmetries of simple \(A \mathbb{T}\)-algebras ⋮ Tracial oscillation zero and \(\mathcal{Z}\)-stability ⋮ A decomposition theorem for real rank zero inductive limits of 1-dimensional non-commutative CW complexes ⋮ Approximate unitary equivalence in simple $C^{*}$-algebras of tracial rank one ⋮ Simple \(C^*\)-algebras with locally bounded irreducible representation ⋮ Smooth crossed product of minimal unique ergodic diffeomorphisms of a manifold and cyclic cohomology ⋮ On locally AH algebras ⋮ Unital extensions of AF-algebras by purely infinite simple algebras ⋮ Tracial approximation is stable ⋮ Classification of simple \(C^*\)-algebras: Inductive limits of matrix algebras over one-dimensional spaces ⋮ Regularity properties of certain crossed product \(C^*\)-algebras ⋮ ALMOST MULTIPLICATIVE MORPHISMS AND K-THEORY ⋮ Topologically conjugate classifications of the translation actions on low-dimensional compact connected Lie groups ⋮ Simple generalized inductive limits of \(C\)*-algebras ⋮ Dimension growth for \(C^{*}\)-algebras ⋮ Completeness of the isomorphism problem for separable \(C^\ast\)-algebras ⋮ Extensions of certain real rank zero \(C^*\)-algebras ⋮ Recasting the Elliott conjecture ⋮ Extensions of AH algebras with the ideal property ⋮ C*-ALGEBRAS OF TRIVIAL K-THEORY AND SEMILATTICES ⋮ Similarity classification of holomorphic curves ⋮ A separable Brown-Douglas-Fillmore theorem and weak stability ⋮ The UCT problem for nuclear \(C^\ast\)-algebras ⋮ Infinite simple \(C^*\)-algebras and reduced cross products of abelian \(C^*\)-algebras and free groups ⋮ Approximated by finite-dimensional homomorphisms into simple $C^*$-algebras with tracial rank one ⋮ The classification of certain ASH C*-algebras of real rank zero ⋮ A𝕋-algebras from fiberwise essentially minimal zero-dimensional dynamical systems ⋮ Crossed products and minimal dynamical systems ⋮ The linear span of projections in AH algebras and for inclusions of \(C^\ast\)-algebras ⋮ 𝐶*-algebras and their nuclear dimension ⋮ Equivalence relations of AF-algebra extensions ⋮ Classification of \(C^*\)-algebras of real rank zero and unsuspended \(E\)-equivalence types ⋮ On the classification of simple inductive limit \(C^{*}\)-algebras. II: The isomorphism theorem ⋮ Simple \(C^{*}\)-algebras with locally finite decomposition rank ⋮ Tracial approximation in simple -algebras ⋮ Regularity properties in the classification program for separable amenable C*-algebras ⋮ Topological complexity of certain classes of \(C^\ast\)-algebras ⋮ A total Cuntz semigroup for \(C^*\)-algebras of stable rank one ⋮ The unitary Cuntz semigroup on the classification of non-simple \(C^\ast\)-algebras ⋮ Classification of extensions of torus algebra. II ⋮ Unitary groups as a complete invariant ⋮ K-theoretic rigidity and slow dimension growth ⋮ Asymptotic unitary equivalence and classification of simple amenable \(C^{\ast}\)-algebras ⋮ Purely infinite corona algebras and extensions ⋮ On classification of non-unital amenable simple C*-algebras. II ⋮ On invariants of \(\mathrm C^{\ast}\)-algebras with the ideal property ⋮ Tracial Rokhlin property for automorphisms on simple -algebras ⋮ Dimension, comparison, and almost finiteness ⋮ Some \(K_0\)-monoid properties preserved by tracial approximation ⋮ Commutators and linear spans of projections in certain finite \(C^\ast\)-algebras ⋮ Projection decomposition in multiplier algebras ⋮ Simple nuclear \(C^{*}\)-algebras of tracial topological rank one ⋮ A unitary Cuntz semigroup for \(C^\ast \)-algebras of stable rank one ⋮ A REMARK ON THE TRACIAL ROKHLIN PROPERTY ⋮ Crossed products by minimal homeomorphisms ⋮ Certain Cuntz semigroup properties of certain crossed product \(C^*\)-algebras ⋮ On tracial approximation ⋮ Quasidiagonality of nuclear \(\mathrm{C}^\ast\)-algebras ⋮ Lifting \(KK\)-elements, asymptotic unitary equivalence and classification of simple C\(^*\)-algebras ⋮ Approximations of \(C^{*}\)-algebras and the ideal property ⋮ Inductive limit of direct sums of simple TAI algebras ⋮ MORPHISMS OF SIMPLE TRACIALLY AF ALGEBRAS ⋮ On the decomposition theorems for \(C^*\)-algebras ⋮ The classification of simple separable unital \(\mathcal{Z}\)-stable locally ASH algebras ⋮ On a lifting question of Blackadar ⋮ Mean dimension and AH-algebras with diagonal maps ⋮ Quotient semigroups and extension semigroups ⋮ Classification of a class of crossed product \(C^{*}\)-algebras associated with residually finite groups ⋮ The \(KK\)-lifting problem for dimension drop interval algebras ⋮ Classification of simple \(C^*\)-algebras of tracial topological rank zero ⋮ Homomorphisms between \(C^*\)-algebra extensions ⋮ The Rokhlin property and the tracial topological rank ⋮ Finite sums and products of commutators in inductive limit \(C^ \ast\)- algebras ⋮ Isomorphism of extensions of \(C(\mathbb{T} ^{2})\) ⋮ An approximate universal coefficient theorem ⋮ Homotopy of unitaries in simple \(C^{*}\)-algebras with tracial rank one ⋮ \(A\mathbb T\) structure of \(AH\) algebras with the ideal property and torsion free \(K\)-theory ⋮ The extensions of \(C^{*}\)-algebras with tracial topological rank no more than one ⋮ Real \(C^*\)-algebras, united \(KK\)-theory, and the universal coefficient theorem ⋮ Twisted \(k\)-graph algebras associated to Bratteli diagrams ⋮ \({\mathbb{Z}}\)-actions on AH algebras and \({\mathbb{Z}^2}\)-actions on AF algebras ⋮ The homoclinic and heteroclinic C*-algebras of a generalized one-dimensional solenoid ⋮ The commutant and similarity invariant of analytic Toeplitz operators on Bergman space ⋮ On ideals and quotients of \(A{\mathcal T}\)-algebras ⋮ A class of simple \(C^*\)-algebras with stable rank one ⋮ The Elliott conjecture for Villadsen algebras of the first type ⋮ TOPOLOGICAL STABLE RANK OF INCLUSIONS OF UNITAL C*-ALGEBRAS ⋮ Almost commuting unitaries and classification of purely infinite simple \(C^*\)-algebras ⋮ The AF structure of non commutative toroidal ℤ/4ℤ orbifolds ⋮ Hausdorffified algebraic \(K_1\)-groups and invariants for \(C^\ast\)-algebras with the ideal property ⋮ CLASSIFICATION OF EXTENSIONS OF A𝕋-ALGEBRAS ⋮ A CLASSIFICATION OF NON-SIMPLE C*-ALGEBRAS OF TRACIAL RANK ONE: INDUCTIVE LIMITS OF FINITE DIRECT SUMS OF SIMPLE TAI C*-ALGEBRAS ⋮ Crossed products by finite group actions with certain tracial Rokhlin property ⋮ The classification of certain non-simple \(C^*\)-algebras of tracial rank zero ⋮ CERTAIN APERIODIC AUTOMORPHISMS OF UNITAL SIMPLE PROJECTIONLESS C*-ALGEBRAS ⋮ Rokhlin actions of finite groups on UHF-absorbing $\mathrm {C}^*$-algebras
This page was built for publication: On the classification of \(C^*\)-algebras of real rank zero. II
