Homogeneous C*-algebras

Mikhail Shchukin Belarusian State University

Every homogeneous C^{∗}-algebra corresponds to the algebraic fibre bundle. C^{∗}- algebra is called non-trivial if the corresponding algebraic fibre bundle is non-trivial. All C^{∗}-algebras generated by idempotents that studied before corresponded to the trivial algebraic fibre bundles. In the work was showed that every homogeneous separable non-commutative C^{∗}-algebra can be generated by idempotents. It is follows from here that we need to study the topology properties of C^{∗}-algebras generated by idempotents to describe such algebras properly. Also in the work we found the minimal number of idempotent generators for every homogeneous C^{∗}-algebra A with the set of maximal ideals homeomorphic to the sphere S^{2}.