Simple stably projectionless C*-algebras with generalized tracial rank one

DOI10.4171/JNCG/367zbMath1460.46052arXiv1711.01240OpenAlexW3031374617MaRDI QIDQ784881

Zhuang Niu, Guihua Gong, Huaxin Lin, George A. Elliott

Publication date: 3 August 2020

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.01240

zbMATH Keywords

simple C*-algebrasstably projectionless

Mathematics Subject Classification ID

Classifications of (C^*)-algebras (46L35)

Related Items

Unitary groups and augmented Cuntz semigroups of separable simple 𝒵-Stable C∗-algebras ⋮ Nonamenable simple -algebras with tracial approximation ⋮ Nuclear dimension of simple stably projectionless \(C^\ast\)-algebras ⋮ The classification of Rokhlin flows on \(\mathrm{C}^*\)-algebras ⋮ On classification of nonunital amenable simple \(C^\ast\)-algebras. III: The range and the reduction ⋮ Constructing C*-diagonals in AH-algebras ⋮ Chaotic tracial dynamics ⋮ Comparison properties for asymptotically tracially approximation \(C^*\)-algebras ⋮ Equivariant Kirchberg-Phillips type absorption for the Razak-Jacelon algebra ⋮ Hereditary uniform property \(\Gamma\) ⋮ A characterization of the Razak-Jacelon algebra ⋮ Tracial oscillation zero and \(\mathcal{Z}\)-stability ⋮ The classification of simple separable KK-contractible C*-algebras with finite nuclear dimension ⋮ On classification of non-unital amenable simple C*-algebras. II ⋮ Every classifiable simple C\(^*\)-algebra has a Cartan subalgebra ⋮ The Cuntz-Toeplitz algebras have nuclear dimension one

Cites Work

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• Quasidiagonality of nuclear \(\mathrm{C}^\ast\)-algebras
• Nuclear dimension and \(\mathcal{Z}\)-stability of pure \(C^{\ast}\)-algebras
• Classification of inductive limits of 1-dimensional NCCW complexes
• Dimension functions and traces on C*-algebras
• Equivalence and traces on \(C^*\)-algebras
• Traces on simple AF C*-algebras
• 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
• Stable isomorphism of hereditary subalgebras of \(C^*\)-algebras
• Lifting solutions to perturbing problems in \(C^*\)-algebras
• Classification of certain infinite simple \(C^*\)-algebras
• A universal multicoefficient theorem for the Kasparov groups
• A classification theorem for nuclear purely infinite simple \(C^*\)-algebras
• Nuclear dimension, \(\mathcal Z\)-stability, and algebraic simplicity for stably projectionless \(C^\ast\)-algebras
• Simple nuclear \(C^{*}\)-algebras of tracial topological rank one
• On tracial approximation
• On topologically finite-dimensional simple \(C^*\)-algebras
• Localizing the Elliott conjecture at strongly self-absorbing \(C^*\)-algebras
• On the positive tracial cones of simple stably projectionless \(C^*\)-algebras
• REMARKS ON -STABLE PROJECTIONLESS C*-ALGEBRAS
• Homomorphisms from AH-algebras
• The cone of lower semicontinuous traces on a C*-algebra
• ON THE CLASSIFICATION OF NUCLEAR C^*-ALGEBRAS
• Classifying crossed product C*-algebras
• Dimension and Stable Rank in the K -Theory of C^* -Algebras
• The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras
• The Cuntz semigroup as an invariant for C*-algebras
• The Jiang–Su algebra revisited
• Simple C ∗ -Algebras with Continuous Scales and Simple Corona Algebras
• Homomorphisms between finite direct sums of circle algebras
• The structure of multiplication and addition in simple $C^*$-algebras.
• Fragility of Subhomogeneous C *-Algebras with One-Dimensional Spectrum
• Traces and simple C* -algebras with tracial topological rank zero
• Embedding of exact C* -algebras in the Cuntz algebra 𝒪2
• ALMOST MULTIPLICATIVE MORPHISMS AND K-THEORY
• On the Classification of Simple Stably Projectionless C^*-Algebras
• THE STABLE AND THE REAL RANK OF ${\mathcal Z}$-ABSORBING C*-ALGEBRAS
• COVERING DIMENSION AND QUASIDIAGONALITY
• Simple corona $C^*$-algebras
• On the geometry of the unit ball of a C*- algebra.
• A simple, monotracial, stably projectionless C *‐algebra
• Rotation Algebras and the Exel Trace Formula
• On locally AH algebras
• From the Basic Homotopy Lemma to the Classification of 𝐶*-algebras
• Three Applications of the Cuntz Semigroup