Exactness of the Fock space representation of the q-commutation relations

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

References in corpus (2)

• Non injectivity of the q-deformed von Neumann algebra
• Factoriality of Bozejko-Speicher von Neumann algebras

Cited by in corpus (8)

• Fock representations of $Q$-deformed commutation relations
• Fock representations of multicomponent (particularly non-Abelian anyon) commutation relations
• Ultraproduct methods for mixed $q$-Gaussian algebras
• On $q$-tensor product of Cuntz algebras
• Free monotone transport for infinite variables
• An application of free transport to mixed $q$-Gaussian algebras
• CCR and CAR algebras are connected via a path of Cuntz-Toeplitz algebras
• Faithfulness of the Fock representation of $C^{\ast }$-algebra generated by $q_{ij}$-commuting isometries