Mixing subalgebras of finite von Neumann algebras

Jan Cameron (Vassar College)

Tuesday 8th June, 2010 16:00-17:00 214

Abstract

It is well-known that generalizations of mixing properties of probability measure-preserving transformations can be defined in dynamical systems arising from the action of a countable, discrete group on a von Neumann algebra. Recently, Jolissaint and Stalder observed that the mixing properties of the action of a discrete abelian group on a von Neumann algebra are encoded by certain analytical and algebraic properties of the associated crossed product von Neumann algebra. Using their definitions as a starting point, we introduce and study various mixing properties of inclusions N \subset M of finite von Neumann algebras. This perspective yields some applications to ergodic theory, for example, a new generalization of a result of Halmos on automorphisms of a compact group. We also exhibit connections between mixing properties von Neumann subalgebras and their normalizers, and a number of new examples of mixing phenomena in the operator algebra setting. This is ongoing joint work with Junsheng Fang (Texas A&M university) and Kunal Mukherjee (Institute of Mathematical Sciences, Chennai).

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