Non trivial C*-Algebras generated by three idempotents

M. Shchukin

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 the idempotents that studied before correspondes to the trivial algebraic fibre bundles. I show that non-trivial C*-algebras of any dimension n ³ 2 can be generated by three idempotents. It is follows from here that we need to study the topology properties of C*-algebras generated by the idempotents to describe such algebras.