Mixing and spectral gap relative to Pinsker algebras of Sofic groups

Ben Hayes
University of Virginia

I will discuss the Pinsker algebra of a pmp action of a sofic group. This is a canonical, invariant sigma-algebra which is maximal with respect to having the correspond factor have zero entropy. I will deduce spectral properties of the whole action relative to its Pinsker factor, including mixing and spectral gap. I will discuss how these are analogous to my results on 1-bounded entropy in the von Neumann algebra case, which have applications to structural properties of free group factors.

Back to Workshop II: Approximation Properties in Operator Algebras and Ergodic Theory