To any strongly continuous orthogonal representation of \R on a real Hilbert space H_\R, Hiai contructed q-deformed Araki-Woods von Neumann algebra for -1< q < 1, which are von Neuamm algebra arising from non-tracial representation of the q-commutation relations. We prove that if the orthogonal representation is not ergodic then these von Neumann algebras are factors whenever dim(H_\R). In such case, the centralizer of the quasi-free state has trivial relative commutant.
Date and Time : 22-09-2017 14:30
Venue : PSB 2214
Speaker : P. G. Bikram, NISER Bhubaneswar