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

Let A be a n-homogeneous $(n \geqslant 4)$ C*-algebra. Further, suppose the space
primA of primitive ideals for the algebra A is homeomorphic to a two-dimensional oriented
manifold. In this case, the algebra A can be generated by three idempotents. The algebra A can
not be generated by two idempotents.

Keywords: C*-algebra, primitive ideals, base space, algebraic bundle, operator algebra,
irreducible representation