Factoriality of Bozejko-Speicher von Neumann algebras
Operator Algebras
2009-11-10 v2 Quantum Algebra
Abstract
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_i l_j^*-q l_j^* l_i=delta_{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 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 II_1 and type III case.
Keywords
Cite
@article{arxiv.math/0307201,
title = {Factoriality of Bozejko-Speicher von Neumann algebras},
author = {Piotr Sniady},
journal= {arXiv preprint arXiv:math/0307201},
year = {2009}
}
Comments
8 pages. NEW IN VERSION 2: considered factors do not have the property Gamma