2016/06/15 by Bikram, Panchugopal, Mukherjee, Kunal
#FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1606.04752
To any strongly continuous orthogonal representation of \R on a real Hilbert space \CH_\R, Hiai constructed q-deformed Araki-Woods von Neumann algebras for -1< q< 1, which are W∗-algebras arising from non tracial representations of the q-commutation relations, the latter yielding an interpolation between the Bosonic and Fermionic statistics. We prove that if the orthogonal representation is not ergodic then these von Neumann algebras are factors whenever dim(\CH_\R)≥ 2 and q∈ (-1,1). In such case, the centralizer of the q-quasi free state has trivial relative commutant. In the process, we study `generator masas' in these factors and establish that they are strongly mixing. The analysis is inspired by a previous work of É. Ricard on Bo\overset.zejko-Speicher's factors \citeER and measure-multiplicity invariant of masas introduced by K. Dykema, A. Sinclair and R. Smith in \citeDSS06.