The homotopy groups of the automorphism group of Kirchberg algebras

DOI10.4171/JNCG/3zbMath1144.46047MaRDI QIDQ947855

Marius Dǎdǎrlat

Publication date: 7 October 2008

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

Full work available at URL: http://www.ems-ph.org/journals/show_pdf.php?issn=1661-6952&vol=1&iss=1&rank=3

zbMATH Keywords

\(K\)-theoryautomorphismshomotopypurely infinite \(C^*\)-algebras

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) General theory of (C^*)-algebras (46L05) Automorphisms of selfadjoint operator algebras (46L40) Homotopy groups of special spaces (55Q52)

Related Items (11)

The C*-algebra of a vector bundle ⋮ A Dixmier-Douady theory for strongly self-absorbing \(C^\ast\)-algebras ⋮ Topological complexity of certain classes of \(C^\ast\)-algebras ⋮ Classification of 𝒪_{∞}-Stable 𝒞*-Algebras ⋮ A new proof of Kirchberg's \(\mathcal{O}_2\)-stable classification ⋮ The homotopy groups of the automorphism groups of Cuntz-Toeplitz algebras ⋮ \(\mathbb Z^2\)-actions on Kirchberg algebras ⋮ Poly-\(\mathbb{Z}\) group actions on Kirchberg algebras. II ⋮ A weak homotopy equivalence type result related to Kirchberg algebras ⋮ The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra ⋮ A topological invariant for continuous fields of Cuntz algebras II

Cites Work

• Continuous fields of \(C^*\)-algebras over finite dimensional spaces
• The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor
• Equivariant KK-theory and the Novikov conjecture
• Une notion de nucléarité en K-théorie (d'après J. Cuntz). (A notion of nuclearity in K-theory (in the sense of J. Cuntz))
• A class of C*-algebras and topological Markov chains
• K-theory for certain C*-algebras
• A class of C*-algebras and topological Markov chains II: Reducible chains and the Ext-functor for C*-algebras
• Certain \(C^*\)-algebras with real rank zero and their corona and multiplier algebras. I
• Homology for zero-dimensional nonwandering sets
• The structure of \(C^*\)-algebras associated with hyperbolic dynamical systems
• Non-simple purely infinite \(C^{*}\)-algebras: The Hausdorff case.
• A classification theorem for nuclear purely infinite simple \(C^*\)-algebras
• Purely infinite $C^*$-algebras arising from dynamical systems
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