Department of Mathematics

The q-deformed Gaussian von Neumann algebras or more generally the Yang-Baxter deformed Gaussian von Neumann algebras were introduced in 1994 by Marek Bozejko and Roland Speicher as a deformation of free Gaussian algebras (isomorphic to the free group factors). In 2023, da Silva and Lechner generalized this Yang-Baxter deformation construction to the nontracial cases and the resulting algebras are called the twisted Araki-Woods algebras. We explain how the existence of conjugate variables implies the factoriality of finitely generated twisted Araki-Woods algebras using the powerful results of Brent Nelson on nontracial finite free fisher information. This generalizes the corresponding results for q-Gaussians by A. Miyagawa and R. Speicher and for q-Araki-Woods by M. Kumar, A. Skalski and M. Wasilewski. Should time permit, we will also talk about certain sufficient conditions for those algebras to have the Akemann-Ostrand property.