THE UNITAL EXT-GROUPS AND CLASSIFICATION OFC*-ALGEBRAS

DOI10.1017/S0017089519000053zbMath1440.46051arXiv1810.10947OpenAlexW2921310027MaRDI QIDQ5203864

James Gabe, Efren Ruiz

Publication date: 9 December 2019

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.10947

zbMATH Keywords

\(C^*\)-algebrasExt groups$K$-theory

Mathematics Subject Classification ID

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

Related Items (8)

CCR and CAR algebras are connected via a path of Cuntz-Toeplitz algebras ⋮ Topologizing UCTs for unital extensions ⋮ Double relative commutants in coronas of separable C^*-algebras ⋮ Classification of 𝒪_{∞}-Stable 𝒞*-Algebras ⋮ Unnamed Item ⋮ The extension problem for graph \(C^\ast\)-algebras ⋮ The Cuntz-Toeplitz algebras have nuclear dimension one ⋮ Separating points by inclusions of \(\mathcal{O}_\infty\)

Cites Work

• A note on nonunital absorbing extensions
• The Cuntz semigroup and stability of close \(C^*\)-algebras
• Quasidiagonality of nuclear \(\mathrm{C}^\ast\)-algebras
• The extension problem for graph \(C^\ast\)-algebras
• The complete classification of unital graph \(C^{\ast}\)-algebras: geometric and strong
• Properly infinite \(C(X)\)-algebras and \(K_{1}\)-injectivity
• Classification of extensions of classifiable \(C^{*}\)-algebras
• The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor
• Une notion de nucléarité en K-théorie (d'après J. Cuntz). (A notion of nuclearity in K-theory (in the sense of J. Cuntz))
• K-theory for certain C*-algebras
• \(C^*\)-algebras of real rank zero
• On the classification of inductive limits of sequences of semisimple finite-dimensional algebras
• The completely positive lifting problem for \(C^*\)-algebras
• Classification of extensions of certain \(C^*\)-algebras by their six term exact sequences in \(K\)-theory
• Morphisms of extensions of \(C^*\)-algebras: Pushing forward the Busby invariant
• A classification theorem for nuclear purely infinite simple \(C^*\)-algebras
• On absorbing extensions
• Nuclear dimension and n-comparison
• The Corona Factorization Property, Stability, and the Cuntz Semigroup of a C*-algebra
• Dimension and Stable Rank in the K -Theory of C^* -Algebras
• Semicontinuity and Multipliers of C*-Algebras
• An abstract Voiculescu-Brown-Douglas-Fillmore absorption theorem.
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