caa a22 4500 467932050 CHVBK 20180406152946.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s00020-004-1346-0 doi (NATIONALLICENCE)springer-10.1007/s00020-004-1346-0 The K -Theory of C *-Algebras with Finite Dimensional Irreducible Representations [Elektronische Daten] [John Hunton, Mikhail Shchukin] 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. Birkhäuser Verlag, Basel, 2006 Homogeneous C *-algebra nationallicence K-theory nationallicence finite dimensional representations nationallicence Hunton John Department of Mathematics, University of Leicester, University Road, Leicester, UK aut Shchukin Mikhail Department of Functional Analysis, Belarusian State Univ., Scoriny av. 4, Minsk, Belarus aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/1(2006-01-01), 89-96 0378-620X 54:1<89 2006 54 20 https://doi.org/10.1007/s00020-004-1346-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-004-1346-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hunton John Department of Mathematics, University of Leicester, University Road, Leicester, UK aut NATIONALLICENCE 700 1- Shchukin Mikhail Department of Functional Analysis, Belarusian State Univ., Scoriny av. 4, Minsk, Belarus aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/1(2006-01-01), 89-96 0378-620X 54:1<89 2006 54 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer