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Operator Algebra and Noncommutative Geometry Seminar Series
May 31, 2018 @ 3:30 pm - 4:30 pm
Oh dear! We’ve Fell back into Cartan Subalgebras.
Mr Nicholas Seaton (University of Wollongong)
In 1963, J. Dixmier and A. Douady classified continuous trace $C^*$-algebras with spectrum $T$ up to Morita equivalence by classes in the 3rd Cech cohomology group. In 2011, A. An Heuf, A. Kumjian and A. Sims generalised this to classify Fell algebras. They managed this by looking at their relationship to Cartan subalgebras. In this talk, we will introduce Fell algebras and show that every Fell algebra is Morita equivalent to a $C^*$-algebra with a Cartan subalgebra. If time persists, we will discuss how to build an invariant for Fell algebras with spectrum $X$.