Groups and Operator Algebras Seminar

Speaker: Mateusz Wasilewski (IMPAN)

Title: Recent advances in q-deformed von Neumann algebras

Abstract: In the first part of the talk I will report on a recent non-isomorphism result for q-Gaussian von Neumann algebras (and C*-algebras). The main result (due to Caspers) is that the q-Gaussian von Neumann algebra is not isomorphic to the free group factor in the case of infinitely many generators. I will also discuss a version of this non-isomorphism for the corresponding C*-algebras (due to Borst, Caspers, Klisse, and myself).

In the second part of the talk I will present a recent complete solution to the factoriality problem of q-Araki-Woods algebras, the non-tracial version of the q-Gaussian algebras, obtained in collaboration with Kumar and Skalski. Our approach combines results of Miyagawa and Speicher about conjugate variables for q-Gaussian variables and abstract von Neumann algebraic results of Nelson.

GOA website: https://sites.google.com/view/copenhagen-goa-seminar