The Brauer group of a compact Hausdorff space and $n$-homogeneous $C^{\ast }$-algebras

Abstract:

The structure of all n-homogeneous ${C^\ast }$-algebras with a given compact Hausdorff space X as maximal ideal space is looked at from a cohomological standpoint. Such algebras are matrix algebra bundles over X, and by means of fibrewise tensor products, a group, $B(X)$, analogous to the Brauer group of field theory, is constructed. A partial cohomological description of this group is given. Projective representations of finite groups are used to provide examples where $B(X)$ is precisely computable and non-trivial.