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Exactness of the Fock Space Representation of the q-Commutation Relations

  • Matthew Kennedy
  • Alexandru NicaEmail author
Article

Abstract

We show that for all q in the interval (−1, 1), the Fock representation of the q-commutation relations can be unitarily embedded into the Fock representation of the extended Cuntz algebra. In particular, this implies that the C*-algebra generated by the Fock representation of the q-commutation relations is exact. An immediate consequence is that the q-Gaussian von Neumann algebra is weakly exact for all q in the interval (−1, 1).

Keywords

Creation Operator Cuntz Algebra Generalize Brownian Motion Free Entropy Dimension Left Creation Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Pure Mathematics DepartmentUniversity of WaterlooWaterlooCanada

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