Probabilistic Operator Algebra Seminar: Free products of finite-dimensional von Neumann algebras in terms of free Araki-Woods factors

Seminar | April 15 | 2-4 p.m. | 736 Evans Hall

 Michael Hartglass, Santa Clara University

 Department of Mathematics

A landmark result of Dykema in 1993 classified free products of tracial finite dimensional von Neumann algebras in terms of interpolated free group factors. In 1997, Shlyakhtenko constructed the free Araki-Woods factors, a natural type III analogue of the free group factors. He asked whether arbitrary free products of non-tracial finite-dimensional von Neumann algebras can always be expressed in terms of free Araki-Woods factors. Partial progress on this problem was obtained by Houdayer and Ueda. In this talk we will answer Shlyakhtenko's question in the affirmative. The key tool we use is a non-tracial free graph von Neumann algebra which will be used to realize some of these free products. This is joint work with Brent Nelson.