On 3-homogeneous C*-algebras over two-dimensional oriented manifolds

We consider algebraic bundles over a two-dimensional compact oriented
connected manifold. In 1961 J. Fell, J. Tomiyama, M. Takesaki showed that every n-homogeneous
C^∗-algebra is isomorphic to the algebra of all continuous sections for the appropriate algebraic
bundle. By using this realization we prove in the work that every 3-homogeneous C^∗-algebra over
two-dimensional compact oriented connected manifold can be generated by three idempotents.
Such algebra can not be generated by two idempotents.