Weak Hopf algebra symmetries of C^*-algebra inclusions

Abstract

After a summary on module algebra actions of C^*-weak Hopf algebras we outline the proof of a reconstruction theorem stating that every finite index depth 2 inclusion N < M of unital C^*-algebras with finite dimensional centers is isomorphic to the invariant subalgebra inclusion M^A < M with respect to a regular weak Hopf algebra action. The proof uses the language of C^*-2-categories.