Homotopy of a pair of approximately commuting unitaries in a simple \(C^*\)-algebra

DOI10.1006/jfan.1998.3261zbMath0939.46033OpenAlexW1984261923MaRDI QIDQ1279646

David E. Evans, George A. Elliott, Ola Bratteli, Akitaka Kishimoto

Publication date: 11 April 1999

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

Full work available at URL: https://doi.org/10.1006/jfan.1998.3261

zbMATH Keywords

\(K\)-theoryspectral gaphomotopy\(K_1\)-simple real rank zero \(C^*\)-algebraapproximately commuting unitariesBott obstructionhomotopy lemmasisospectral obstructionsuper-homotopy

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Spectrum, resolvent (47A10) General theory of (C^*)-algebras (46L05)

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Cites Work

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• K-theory for certain C*-algebras
• Invariants of almost commuting unitaries
• \(C^*\)-algebras of real rank zero
• Derivations of matroid C\(^*\)-algebras. II
• Stable isomorphism of hereditary subalgebras of \(C^*\)-algebras
• Simple \(C^*\)-algebras generated by isometries
• Classification of direct limits of generalized Toeplitz algebras
• Approximately unitarily equivalent morphisms and inductive limit \(C^*\)- algebras
• Almost commuting unitary elements in purely infinite simple \(C^*\)- algebras
• Classification of certain infinite simple \(C^*\)-algebras. II
• Exponential rank of \(C^{\ast}\)-algebras with real rank zero and the Brown-Pedersen conjectures
• On the classification of C*-algebras of real rank zero.
• K-Theory and Asymptotically Commuting Matrices
• A Property of Purely Infinite Simple C ∗ -Algebras
• Extensions of Inductive Limits of Circle Algebras
• Classification of direct limits of even Cuntz-circle algebras