Ilja Gogić

The class of commutative C*-algebras was fully described in the early days of the development of the theory of operator algebras: these are precisely algebras of continuous complex-valued functions on locally compact Hausdorff spaces that vanish at infinity. After commutative, the next simplest class are the homogeneous C*-algebras, i.e. C*-algebras whose all irreducible representations are of the same finite dimension. However, the problem of classification of such algebras becomes considerably more complicated due to certain topological phenomena which do not occur in the commutative case. In this talk we will present the overview of homogeneous C*-algebras with an emphasis on some more recent results.