IISER - TVM

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SEMINAR - q-deformed Araki-Woods von Neumann algebra

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.

Event Date : 2017-09-22