The minimal number of idempotent generators for $3$-homogeneous $\mathrm{C^*}$-algebra over two-dimensional compact oriented manifold

Every $3$-homogeneous $\mathrm{C^*}$-algebra over two-dimensional compact oriented manifold can be realized as algebra of all continuous sections for the appropriate algebraic bundle. In the work we prove that such algebra can be generated by three idempotent elements from the algebra.