, Volume 210, Issue 3, pp 685-701

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

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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.

Received: 22 April 1999 / Accepted: 3 October 1999