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K-Theory for Operator Algebras
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TLDR
A survey of topological K-theory can be found in this paper, where the authors present a survey of applications to geometry and topology, including the Pimsner-Voiculescu exact sequence and Connes' Thorn isomorphism.Abstract:
I. Introduction To K-Theory.- 1. Survey of topological K-theory.- 2. Overview of operator K-theory.- II. Preliminaries.- 3. Local Banach algebras and inductive limits.- 4. Idempotents and equivalence.- III. K0-Theory and Order.- 5. Basi K0-theory.- 6. Order structure on K0.- 7. Theory of AF algebras.- IV. K1-Theory and Bott Periodicity.- 8. Higher K-groups.- 9. Bott Periodicity.- V. K-Theory of Crossed Products.- 10. The Pimsner-Voiculescu exact sequence and Connes' Thorn isomorphism.- 11. Equivariant K-theory.- VI. More Preliminaries.- 12. Multiplier algebras.- 13. Hilbert modules.- 14. Graded C*-algebras.- VII. Theory of Extensions.- 15. Basic theory of extensions.- 16. Brown-Douglas-Fillmore theory and other applications.- VIII. Kasparov's KK-Theory.- 17. Basic theory.- 18. Intersection product.- 19. Further structure in KK-theory.- 20. Equivariant KK-theory.- IX. Further Topics.- 21. Homology and cohomology theories on C*-algebras.- 22. Axiomatic K-theory.- 23. Universal coefficient theorems and Kunneth theorems.- 24. Survey of applications to geometry and topology.read more
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Journal ArticleDOI
Full regularity for a c*-algebra of the canonical commutation relations
TL;DR: In this paper, a C*-algebra which can reproduce the canonical commutation relations of a countably dimensional symplectic space (S, B) and its representation set is exactly the full set of regular representations of the CCRs is constructed.
Journal ArticleDOI
Equivariant KK-Theory and C*-Extensions
TL;DR: In this article, a description of equivariant KK-theory in terms of extensions of C∗-algebras has been given, which is based on an extension of the original KK theory.
Journal ArticleDOI
E-theory for C⁎-algebras over topological spaces
Marius Dadarlat,Ralf Meyer +1 more
TL;DR: In this article, the authors define E-theory for separable C ⁎ -algebras over second countable topological spaces and establish its basic properties, including an approximation theorem that relates the Etheory over a general space to the e-theories over finite approximations to this space.
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K-Theory for Real C*-algebras via Unitary Elements with Symmetries
TL;DR: In this article, it was shown that all eight KO groups for a real C*-algebra can be constructed from homotopy classes of unitary matrices that respect a variety of symmetries.
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Localizing the Elliott conjecture at strongly self-absorbing C*-algebras
TL;DR: In this paper, the concept of localizing the Elliott conjecture at strongly self-absorbing C*-algebras was introduced, and the class of separable, unital, simple, simple and simple C *-algesas with locally finite decomposition rank and UCT, and for which projections separate traces, satisfies the conjecture localized at the Jiang-Su algebra Z.