The von Neumann algebra generated by t-gaussians

We study the $t$-deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if $t$ sufficiently close to 1, then these algebras do not depend on $t$. In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness.