Exactness of the Fock space representation of the q-commutation relations
arXiv:1009.0508 · doi:10.1007/s00220-011-1323-9
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).
20 pages