The K-Theory of C
*-Algebras with Finite Dimensional Irreducible Representations |
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Authors: | John Hunton Mikhail Shchukin |
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Institution: | (1) Department of Mathematics, University of Leicester, University Road, Leicester, UK;(2) Department of Functional Analysis, Belarusian State Univ., Scoriny av. 4, Minsk, Belarus |
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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. |
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Keywords: | Primary 46L80 Secondary 16G30 |
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