REMARKS ON FACTORIALITY AND q-DEFORMATIONS

We prove that the mixed q-Gaussian algebra Gamma(Q)(H-R) associated to a real Hilbert space H-R and a real symmetric matrix Q = (q(ij)) with sup vertical bar q(ij)vertical bar < 1, is a factor as soon as dim H-R >= 2. We also discuss the factoriality of q-deformed Araki-Woods algebras, in particular showing that the q-deformed Araki-Woods algebra Gamma(q)(H-R, U-t) given by a real Hilbert space H-R and a strongly continuous group Ut is a factor when dim H-R >= 2 and U-t admits an invariant eigenvector.