KK-theory of reduced free-product \(C^*\)-algebras

DOI10.1215/S0012-7094-96-08229-0zbMath0863.46046OpenAlexW2071830724MaRDI QIDQ1919642

Emmanuel Germain

Publication date: 3 June 1997

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

Full work available at URL: https://doi.org/10.1215/s0012-7094-96-08229-0

zbMATH Keywords

states\(KK\)-theory\(KK\)-groups\(K\)-nuclear \(C^*\)-algebras\(K\)-pointed \(C^*\)-algebra\(K\)-theoretical equivalencereduced free-product \(C^*\)-algebra

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Kasparov theory ((KK)-theory) (19K35)

Related Items

\(K\)-amenability for amalgamated free products of amenable discrete quantum groups ⋮ Classifying right-angled Hecke \(\mathrm{C}^\ast\)-algebras via \(K\)-theoretic invariants ⋮ The KK-theory of fundamental C*-algebras ⋮ The KK-theory of amalgamated free products ⋮ A simple separable exact \(C^*\)-algebra not anti-isomorphic to itself ⋮ On the KK-theory and the \(E\)-theory of amalgamated free products of \(C^{\ast}\)-algebras. ⋮ Purely infinite simple reduced \(C^*\)-algebras of one-relator separated graphs ⋮ C*-algebras from planar algebras I: Canonical C*-algebras associated to a planar algebra ⋮ \(K\)-amenability of HNN extensions of amenable discrete quantum groups ⋮ C\(^*\)-algebras of separated graphs ⋮ Graphs of quantum groups and \(K\)-amenability ⋮ Relative nuclearity for \({C}^\ast\)-algebras and \(KK\)-equivalences of amalgamated free products ⋮ ON THE STRUCTURE OF SOME REDUCED AMALGAMATED FREE PRODUCT C*-ALGEBRAS ⋮ Simplicity and the stable rank of some free product C*-algebras ⋮ \(KK\)-theory for some graph \(C^\ast\)-algebras ⋮ Topological entropy of free product automorphisms

Cites Work

• K-theory for certain group \(C^*\)-algebras
• KK-groups of crossed products by groups acting on trees
• The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor
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• On the contractability of the unitary group of the Hilbert space over a C*-algebra
• Kasparov's bivariant \(K\)-theory and applications
• \(K\)-theory for partial crossed products by discrete groups
• K-theoretic amenability for \(SL_ 2({\mathbb{Q}}_ p)\), and the action on the associated tree
• The \(K\)-groups of the \(C^*\)-algebra of a semicircular family
• Free Products of C ∗ -Algebras
• THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
• K-theoretic amenability for discrete groups.
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