Master's Thesis Seminar

Wednesday, September 7, 2016 3:00 pm - 3:00 pm EDT (GMT -04:00)

Se-Jin Sam Kim, Pure Mathematics, University of Waterloo

"Crossed products and Morita equivalence"

The talk will consist of three parts. Firstly, we will establish some basic notions of crossed product $C^*$-algebras, with a focus on the irrational rotation algebras.

Next, we will talk about $C^*$-correspondences and (strong) Morita equivalence. We will see that $C^*$-correspondences are a kind of partial morphism between two $C^*$-algebras and that strong Morita equivalence are a kind of partial isomorphism which preserve properties such as the ideal structure and K-theory.

Finally, to connect the two topics, we will present Green's imprimitivity theorem, which is a machinery that gives us Morita equivalence for crossed products of a certain type. If time permits, we will see how this machinery applies to irrational rotation algebras, a theorem of Stone and von Neumann, and the Takesaki-Takai duality.