Lecture Details
Name: John Quigg (Arizona State University)Speaking: Wed 8th May 11:30 - 11:55Title: The Pedersen rigidity problemAbstract: Given an action of a locally compact group $G$ on a $C^*$-algebra $A$, the Imai-Takai duality theorem recovers the action up to Morita equivalence from the dual coaction on the crossed product. Given a bit more information, Landstad duality recovers the action up to isomorphism. In between these, by modifying a theorem of Pedersen, we prove that the action is recovered up to outer conjugacy from the dual coaction and the position of $A$ in the crossed product. Our search (still unsuccessful, somehow irritating) for examples showing the necessity of this latter condition has led us to formulate the ``Pedersen Rigidity problem''. We present numerous situations where the condition is redundant, including $G$ discrete or $A$ stable or commutative. The most interesting of these ``no-go theorems'' is for locally unitary actions of abelian groups on continuous-trace algebras. This is joint work with Steve Kaliszewski and Tron Omland.