Wick Product for Commutation Relations Connected with Yang–Baxter Operators and New Constructions of Factors

Abstract:

We analyze a certain class of von Neumann algebras generated by selfadjoint elements , for satisfying the general commutation relations:

Such algebras can be continuously embedded into some closure of the set of finite linear combinations of vectors , where is an orthonormal basis of a Hilbert space . The operator which represents the vector is denoted by and called the “Wick product” of the operators . We describe explicitly the form of this product. Also, we estimate the operator norm of for . Finally we apply these two results and prove that under the assumption all the von Neumann algebras considered are II ₁ factors.