The K-Theory of C*-Algebras with Finite Dimensional Irreducible Representations

Hunton, John; Shchukin, Mikhail

Abstract

We study the K-theory of unital C *-algebras A satisfying the condition that all irreducible representations are finite and of some bounded dimension. We construct computational tools, but show that K-theory is far from being able to distinguish between various interesting examples. For example, when the algebra A is n-homogeneous, i.e., all irreducible representations are exactly of dimension n, then K *(A) is the topological K-theory of a related compact Hausdorff space, this generalises the classical Gelfand-Naimark theorem, but there are many inequivalent homogeneous algebras with the same related topological space. For general A we give a spectral sequence computing K *(A) from a sequence of topological K-theories of related spaces. For A generated by two idempotents, this becomes a 6-term long exact sequence.

Citation

Hunton, J., & Shchukin, M. (2006). The K-Theory of C*-Algebras with Finite Dimensional Irreducible Representations. Integral Equations and Operator Theory, 54(1), https://doi.org/10.1007/s00020-004-1346-0

• Journal Article Type: Article
• Acceptance Date: Nov 1, 2005
• Online Publication Date: Oct 1, 2005
• Publication Date: 2006-01
• Deposit Date: Jul 29, 2019
• Journal: Integral Equations and Operator Theory
• Print ISSN: 0378-620X
• Electronic ISSN: 1420-8989
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 54
• Issue: 1
• DOI: https://doi.org/10.1007/s00020-004-1346-0
• Public URL: https://durham-repository.worktribe.com/output/1326406