On the \(K\)-theory of \(C^*\)-algebras of principal groupoids

DOI10.1216/rmjm/1181071727zbMath0934.46067OpenAlexW2017020292MaRDI QIDQ1293544

Ian F. Putnam

Publication date: 25 April 2000

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/VOL28-4/CONT28-4/CONT28-4.html

zbMATH Keywords

\(K\)-theorytopological groupoidssubgroupoidsfactor groupoidsKasparov \(KK\)-theoryRenault's reduced \(C^*\)-algebra

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) (L^1)-algebras on groups, semigroups, etc. (43A20)

Related Items

\(K\)-theory of the chair tiling via \(AF\)-algebras, Cancellation and stable rank for direct limits of recursive subhomogeneous algebras, Constructing minimal homeomorphisms on point-like spaces and a dynamical presentation of the Jiang-Su algebra, Long exact sequences of homology groups of étale groupoids, Non-commutative methods for the K-theory of \(C^*\)-algebras of aperiodic patterns from cut-and-project systems, \(K\)-theory of two-dimensional substitution tiling spaces from \textit{AF}-algebras, Classifiable \(\mathrm{C}^*\)-algebras from minimal \(\mathbb{Z} \)-actions and their orbit-breaking subalgebras, Families of type III KMS states on a class of \(C^*\)-algebras containing \(O_n\) and \({\mathcal Q}_{\mathbb N}\), Some classifiable groupoid \(C^{*}\)-algebras with prescribed \(K\)-theory, Crossed products of the Cantor set by free minimal actions of \(\mathbb Z^d\), A general Banach-Stone type theorem and applications, Decomposition rank of approximately subhomogeneous \(C^*\)-algebras, ON GENERALIZED UNIVERSAL IRRATIONAL ROTATION ALGEBRAS AND ASSOCIATED STRONGLY IRREDUCIBLE OPERATORS, Minimal dynamical systems on the product of the Cantor set and the circle

Cites Work

• The \(C^*\)-algebras associated with minimal homeomorphisms of the Cantor set
• A groupoid approach to C*-algebras
• Topological methods for C*-algebras. II: Geometric resolutions and the Kuenneth formula
• Circle actions on \(C^*\)-algebras, partial automorphisms, and a generalized Pimsner-Voiculescu exact sequence
• Orbit equivalence, flow equivalence and ordered cohomology
• Index for subfactors
• Preliminary algebras arising from local homeomorphisms.
• Index for 𝐶*-subalgebras
• Inductive Limits of Finite Dimensional C ∗ -Algebras
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