Communications in Mathematical Physics

, Volume 246, Issue 3, pp 561–567 | Cite as

Factoriality of Bo ejko–Speicher von Neumann Algebras

  • Piotr Śniady


We study the von Neumann algebra generated by q–deformed Gaussian elements l i +l * i , where operators l i fulfill the q–deformed canonical commutation relations l il * j ql * jl i ij for −1<q<1. We show that if the number of generators is finite, greater than some constant depending on q, it is a II 1 factor which does not have the property Γ. Our technique can be used for proving factoriality of many examples of von Neumann algebras arising from some generalized Brownian motions, both for the type II 1 and type III case.


Brownian Motion Commutation Relation Canonical Commutation Relation Generalize Brownian Motion Gaussian Element 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WroclawWroclawPoland

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