Homotopy classes of *-homomorphisms between stable \(C^*\)-algebras and their multiplier algebras

DOI10.1215/S0012-7094-90-06104-6zbMath0718.46054OpenAlexW1575157408MaRDI QIDQ2639307

Klaus Thomsen

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1215/s0012-7094-90-06104-6

zbMATH Keywords

additivestablemultiplier algebrasGrothendieck grouphomotopy invariantabelian semigroup of homotopy classes of *- homomorphismsuniversal functor from the category of \(C^ *\)- algebras to the category of abelian groups

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) General theory of (C^*)-algebras (46L05)

Related Items

A Dixmier-Douady theory for strongly self-absorbing \(C^\ast\)-algebras, A stably contractible 𝐶*-algebra which is not contractible, On the KK-theory and the \(E\)-theory of amalgamated free products of \(C^{\ast}\)-algebras., \(KK\)-theories for topological algebras, Symmetrization of Cuntz' picture for the Kasparov \(KK\)-bifunctor, Homotopy after tensoring with uniformly hyperfinite \(C^*\)-algebras, The fine structure of the Kasparov groups. I: Continuity of the KK-pairing, Pictures of \(KK\)-theory for real \(C^*\)-algebras and almost commuting matrices, A $KK$-like picture for $E$-theory of $C^*$-algebras, Quasidiagonal extensions and sequentially trivial asymptotic homomorphisms

Cites Work

• On a technical theorem of Kasparov
• Algebraic \(K\)-theory of stable \(C^*\)-algebras
• A characterization of KK-theory
• Stable isomorphism of hereditary subalgebras of \(C^*\)-algebras
• THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
• The role of 𝐾-theory in noncommutative algebraic topology
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