To any strongly continuous orthogonal representation of R on a real Hilbert space HR, 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(HR)≥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. © 2017