To any strongly continuous orthogonal representation of real line R on a real Hilbert space H , Hiai constructed q-deformed Araki-Woods von Neumann algebras for −1 < q <1, which are von Neumann algebras arising from non tracial representations of the q-commutation relations, the latter yielding an interpolation between Bosonic and Fermionic statistics. We settle that these von Neumann algebras are factors whenever dim(H ) ≥ 3 and completely determine their type. In the process we obtain and discuss ‘generator masas’ in these factors and establish that they are strongly mixing.
School of Mathematical Sciences
NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050