FACTORIALITY AND FULLNESS OF q-ARAKI-WOODS VON NEUMANN ALGEBRAS

We discuss the factoriality, non-injectivity, and fullness questions of q-Araki-Woods von Neumann algebras, constructed by Hiai. These algebras are non-tracial counterparts of q-Gaussian algebras, which combine the q-deformations of free-group factors due to Bożejko, Kummerer and Speicher, and quasi-free deformations of Shlyakhtenko. We will discuss our approach based on conjugate/dual variables towards the mentioned problems. This is joint work with Adam Skalski and Mateusz Wasilewski, and with Simeng Wang.