OA seminar: Jon P Bannon
Speaker: Jon Bannon (Sienna College).
Title: Full factors and co-amenable inclusions
Abstract: If a factor is full then every approximately inner automorphism is inner. We have the following generalization: If a factor is full, then the any correspondence of weakly equivalent to the trivial correspondence must contain the trivial correspondence. This generalization provides a perspective that allows us to prove that if is a co-amenable inclusion with faithful, normal conditional expectation and a full factor, then there is a nonzero so that is full. As a corollary, this affirmatively answers Problem 3.3.2 of Popa's correspondences preprint from 1986. Furthermore, we use this to prove that if a compact group acts on a full factor then the action is minimal, i.e. . Consequently, for any such action by results of Izumi, Longo and Popa there is a Galois correspondence between the intermediate subalgebras of and fixed point subalgebras of the closed subgroups of .