Factoriality of Bozejko-Speicher von Neumann algebras
Abstract
We study the von Neumann algebra generated by q--deformed Gaussian elements li+li* where operators li fulfill the q--deformed canonical commutation relations li lj*-q lj* li=deltaij for -1<q<1. We show that if the number of generators is finite, greater than some constant depending on q, it is a II1 factor which does not have the property Gamma. Our technique can be used for proving factoriality of many examples of von Neumann algebras arising from some generalized Brownian motions, both for type II1 and type III case.
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