On trivial and non-trivial n-homogeneous C* algebras.

Let A be a C-*- algebra for which all irreducible representations are of di mensional n. Then ([F], [TT], [V]) algebra A is isomorphic to algebra of al l continuous sections of an appropriate algebraic bundle E-A. The basis X o f this bundle coincides with the compact of all maximal two-sided ideals of A. We obtain some conditions which provide that EA is trivial and this yie lds that A is isomorphic to the algebra of ail n x n matrix functions conti nuous on X. In the case when X = S-n is a sphere we describe the set of alg ebraic bundles over X and algebraic structures on this set. Some applicatio ns to algebras generated by idempotents are suggested.