Doctor of Philosophy
School of Mathematics and Applied Statistics
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.
Seaton, Nicholas, The Brauer group for Fell algebras, Doctor of Philosophy thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2021. https://ro.uow.edu.au/theses1/1209
FoR codes (2020)
490408 Operator algebras and functional analysis
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