Communications in Mathematical Physics

, Volume 210, Issue 3, pp 685–701 | Cite as

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

  • Ilona  Kr⊙lak


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.


Hilbert Space Linear Combination Operator Norm Orthonormal Basis Commutation Relation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Ilona  Kr⊙lak
    • 1
  1. 1.Institute of Mathematics, Polish Academy of Sciences, ul. Kopernika 18, 51-617 Wrocław, Poland.¶E-mail:;

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