Bartosz Kwaśniewski
Regular C*-irreducible inclusions and Galois correspondence
An inclusion of C*-subalgebra A in a C*-algebra B is C*-irreducible if all intermediate C*-subalgebras C are simple (Rordam). Such inclusions arise naturally in the study of actions of groups on C*-algebras, either as crossed products (Kishimoto, Cameron-Smith, Amrutam-Kalantar), fixed point algebras (Izumi, Mukohara) or their mixture (Echterhoff-Rordam). In this talk I will discuss C*-irreducible inclusions which are regular in the sense of Kumjian. It follows that hey correspond to outer Fell bundles over discrete groups G, and so up to Morita-equivalence all such inclusions are given by crossed products by an outer group actions. Using a modification of Magajna's separation theorem considered recently by Kennedy-Ursu, I can give a simple proof that the intermediate C*-subalgebras are in bijective correspondence with subgroups of G. This generalises Galois correspondence of Cameron-Smith, and improves upon results of Izumi and Mukohara in the case of abelian groups.
