On trivial and non-trivial n - Homogeneous C* algebras

Anatoly Antonevich, Naum Krupnik

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Abstract

Let A be a C*-algebra for which all irreducible representations are of dimensional n. Then ([F], [TT], [V]) algebra A is isomorphic to algebra of all continuous sections of an appropriate algebraic bundle εA. The basis X of this bundle coincides with the compact of all maximal two-sided ideals of A. We obtain some conditions which provide that εA is trivial and this yields that A is isomorphic to the algebra of all n × n matrix functions continuous on X. In the case when X = Sn is a sphere we describe the set of algebraic bundles over X and algebraic structures on this set. Some applications to algebras generated by idempotents are suggested.

Original languageEnglish
Pages (from-to)172-189
Number of pages18
JournalIntegral Equations and Operator Theory
Volume38
Issue number2
DOIs
StatePublished - 2000

Bibliographical note

Funding Information:
belong to the center of B0 and separate the points of D/S 1. Indeed, if Zl, z2 E D, zl ~ z2 a nd bj(Zl)l--b.~(z~)l (y = 2, 3) then Iz~l--Iz21 and it follows from the equality #2(zl) = #2(z2) that \[zl\[= Iz21 = 1. But such points coincide in D/S x. Therefore the center separates the points of the space D/S 1 and, by Proposition 7.1, B0 = B. It follows from this example that Acknowledgments. The first author wishes to thank the Bar-Ilan University for the invitation and financial support. This work was also partially supported by the Fundamental Research Fund of the Republic of Belarus.

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