Classifying \(C^\ast\)-algebras with both finite and infinite subquotients

DOI10.1016/j.jfa.2013.05.006zbMath1294.46052arXiv1009.4778OpenAlexW2052099369MaRDI QIDQ2637107

Efren Ruiz, Gunnar Restorff, Søren Eilers

Publication date: 19 February 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.4778

zbMATH Keywords

extensionsgraph \(C^*\)-algebras\(C^*\)-algebra classificationfiltered ordered \(K\)-theory

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Classifications of (C^*)-algebras (46L35) Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) (46M18) Kasparov theory ((KK)-theory) (19K35) (K_0) as an ordered group, traces (19K14)

Related Items (8)

The complete classification of unital graph \(C^{\ast}\)-algebras: geometric and strong ⋮ Corrigendum to: ``Classifying \(C^{\ast}\)-algebras with both finite and infinite subquotients ⋮ Unnamed Item ⋮ The ranges of 𝐾-theoretic invariants for nonsimple graph algebras ⋮ Classification of Graph C ∗-Algebras with No More than Four Primitive Ideals ⋮ Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras ⋮ Strong classification of purely infinite Cuntz-Krieger algebras ⋮ Leavitt \(R\)-algebras over countable graphs embed into \(L_{2,R}\).

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Full extensions and approximate unitary equivalence
• On graph \(C^*\)-algebras with a linear ideal lattice
• Classification of extensions of classifiable \(C^{*}\)-algebras
• The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor
• 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
• Stable isomorphism of hereditary subalgebras of \(C^*\)-algebras
• Classification of extensions of certain \(C^*\)-algebras by their six term exact sequences in \(K\)-theory
• The ideal structure of the \(C^*\)-algebras of infinite graphs
• Morphisms of extensions of \(C^*\)-algebras: Pushing forward the Busby invariant
• The \(C^*\)-algebras of arbitrary graphs
• On the classification of nonsimple graph \(C^{*}\)-algebras
• C*-Algebras over Topological Spaces: Filtrated K-Theory
• FILTRATED K-THEORY FOR REAL RANK ZERO C*-ALGEBRAS
• The Corona Factorization Property and refinement monoids
• Classification of Cuntz-Krieger algebras up to stable isomorphism
• Strongly self-absorbing $C^{*}$-algebras
• C*-Algebras over Topological Spaces: The Bootstrap Class
• $S$-regularity and the corona factorization property

This page was built for publication: Classifying \(C^\ast\)-algebras with both finite and infinite subquotients