# John Quigg, Arizona State University (Tempe), USA: "Pedersen Rigidity for Compact Ergodic Actions".

Abstract: Recently, Steve Kaliszewski, Tron Omland, and I have been investigating the following theorem of Pedersen: two actions of a compact abelian group on C*-algebras A and B are outer conjugate if and only if there is an equivariant isomorphism between the crossed products that respects the positions of A and B. We upgraded this to nonabelian groups (using coactions on the crossed products), and then searched for examples showing that the last condition (on the positions of A and B) is necessary. We failed. This lead us to formulate the "Pedersen Rigidity Problem": if the crossed products of A and B are equivariantly isomorphic, are the actions on A and B outer conjugate? We have been finding numerous "no-go theorems", which give various sufficient conditions for Pedersen Rigidity. Quite recently we have done this for ergodic actions of a compact group, assuming that the actions have "full spectrum". In fact, these actions are (not just outer) conjugate if and only if the dual coactions are. I will summarize our progress on the Pedersen Rigidity Problem and outline the proof of the no-go theorem for these compact ergodic full-spectrum actions.