structural aspects of von Neumann algebras arising as graph products (Rolando de Santiago, Purdue University)

Graph products of groups were introduced in E. Green’s thesis in the 90’s as generalizations of Right-Angled Artin Groups. These have become objects of intense study due to their key roles in topology and group theory.  Recently, Caspers and Fima introduced graph products of von Neumann algebras. Since their inception, several structural aspects such as absence of Cartan subalgebras, and classification of tensor products have been established for graph products arising from groups.  Here we describe new progress in this direction, emphasizing characterization of diffuseness, factoriality, and if time, strong 1-boundedness for graph products of a large class of von Neumann algebras.

This is joint work with Ian Charlesworth, Srivatsav Kunnawalkam-Ellayavali,  Ben Hayes, David Jekel, and Brent Nelson.