The Atiyah-Segal completion theorem for \(C^*\)-algebras

DOI10.1007/BF00534138zbMath0709.46034OpenAlexW1976729017MaRDI QIDQ921479

N. Christopher Phillips

Publication date: 1989

Published in: \(K\)-Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00534138

zbMATH Keywords

classifying spaceequivariant K-theorycompact Lie groupAtiyah-Segal completion theoremcrossed product of C*-algebrashomotopy equivariantlong exact sequencesrepresentable K-theory for sigma-C*-algebrasrepresentative K- theory groupstable outer multiplier algebra

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative dynamical systems (46L55)

Related Items (4)

The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ) ⋮ A fixed point decomposition of twisted equivariant K-theory ⋮ Representable K-theory for \(\sigma\)-C\({}^*\)-algebras ⋮ Topology and flux of T-dual manifolds with circle actions

Cites Work

• Construction of universal bundles. II
• Representable K-theory for \(\sigma\)-C\({}^*\)-algebras
• Families of subgroups and completion
• Equivariant K-theory and freeness of group actions on \(C^ *\)-algebras
• A generalization of the Atiyah-Segal completion theorem
• An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R
• Restriction maps in equivariant K-theory
• Equivariant K-theory
• Partitions of unity in the theory of fibrations
• Equivariant \(K\)-theory and completion
• Completely order Isomorphic and Close C^* -Algebras need not BE, ^* -Isomorphic
• Group Extensions and Cohomology for Locally Compact Groups. IV
• Perturbations of C^* -Algebras, II
• K-theoretic amenability for discrete groups.
• BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS
• Perturbations of Von Neumann Algebras I Stability of Type
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