Wick product for commutation relations connected with Yang-Baxter operators and new constructions of factors

We analyze a certain class of von Neumann algebras generated by selfadjoint elements omega(i) = a(i) + a(i)(+), for a(i), a(i)(+) satisfying the general commutation relations: a(i)a(j)(+) = Sigma(r,s)t(js)(ir) a(r)(+)a(s) + delta(ij)Id. Such algebras can be continuously embedded into some closure of the set of finite linear combinations of vectors e(il) x ... x e(ik), where {e(i)} is an orthonormal basis of a Hilbert space H. The operator which represents the vector e(ij) x ... x e(in) is denoted by psi (e(il) x ... x e(in)) and called the "Wick product" of the operators omega(il) ,..., omega(in). We describe explicitly the form of this product. Also, we estimate the operator norm of psi (f) for f is an element of H-xn. Finally we apply these two results and prove that under the assumption dim H = infinity all the von Neumann algebras considered are IIl factors.