Inclusions of C*-algebras

Mikael Rordam  (University of Copenhagen)

9:00-10:20,August 1,2023   文附楼 (Wenfu Building) 219

Abstract:

Much interesting and deep mathematics arise from the study of inclusions of objects (groups, von Neumann algebras, C*-algebras to mention a few friendly examples). In particular, one may wish to understand the collection of all intermediate objects of a given inclusion. In recent literature several examples, mostly arising from dynamics, were given of inclusions of C*-algebras where all intermediate C*-algebras are simple. By analogy with the situation for inclusions of von Neumann algebras, we refer to such inclusions of C*-algebras as being C*-irreducible. However, unlike the von Neumann situation, this property is strictly stronger, and more profound, than being just irreducible (= trivial relative commutant). One can give an algebraic characterization of C*-irreducible inclusions, which again can be used to provide new examples of such inclusions. In this talk I will focus on examples of C*-irreducible inclusions and of classification results for intermediate C*-algebras.

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