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

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.