On n-homogeneous C*-algebras over two-dimensional oriented compact manifolds

Abstract

We consider the n-homogeneous C*-algebras over a two-dimensional compact oriented connected manifold. Suppose A be the n-homogeneous C*-algebra with space of primitive ideals homeomorphic to a two-dimensional connected oriented compact manifold P ( A ). It is well known that the manifold P ( A ) is homeomorphic to the sphere Pk glued together with k handles in the hull-kernel topology. On the other hand, the algebra A is isomorphic to the algebra Γ( E ) of continuous sections for the appropriate algebraic bundle E. The base space for the algebraic bundle is homeomorphic to the set Pk. By using this geometric realization, we described the class of non-isomorphic n-homogeneous ( n ≥ 2) C*-algebras over the set Pk. Also, we calculated the number of non-isomorphic n -homogeneous C*-algebras over the set Pk.