The Brauer group for Fell algebras

In the 1960's, Dixmier and Douady showed that continuous-trace C*-algebras can be classified up to spectral-preserving Morita equivalence. They provided a cohomology group which can track this equivalence. In 2010, an Huef, Kumjian and Sims provided a Dixmier-Douady theory for a more general class of C*-algebras, namely Fell algebras. It follows that there is a group structure on the collection of Morita-equivalence classes of Fell algebras with a given spectrum | the one pulled back from the cohomology group. For continuous-trace C*-algebras, this group structure is explicitly described by a balanced tensor product operation, and the resulting group is called the Brauer group. This thesis aims to describe a Brauer group for Fell algebras. We give an account of the Dixmier-Douady theory for continuous-trace C*-algebras. We then give the full details of the Dixmier-Douady theory of Fell algebras. With this, we will give the construction of the Brauer group for Fell algebras.