Events for 07/19/2023 from all calendars

Workshop in Analysis and Probability Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Zhiyuan Yang, Texas A&M University

Title: A conjugate system for twisted Araki-Woods algebras of finite dimensional spaces

Abstract: The T-twisted Araki-Woods algebra introduced by da Silva and Lechner in 2022 is a quasi-free generalization of the Bożejko-Speicher von Neumann algebra associated with a self-adjoint Yang-Baxter operator T. When T=qF is the q-scaled tensor flip, one obtain the q-Gaussian (q-Araki-Woods) algebra. In this talk, we will begin with the construction of T-deformed Fock space and the crossing symmetric condition on T. We then talk about the conjugate system of twisted Araki-Woods algebras, generalizing the recent results for q-Gaussians by Miyagawa and Speicher in 2022. As a result, we show the factoriality of twisted Araki-Woods algebra when ‖T‖<1, and that for small ‖T‖ it is actually isomorphic to the free Araki-Woods algebra.