CCR and CAR Algebras are Connected Via a Path of Cuntz–Toeplitz Algebras
Journal article, 2023

For q∈ R, | q| < 1 we consider the universal enveloping C∗-algebra of a ∗ -algebra of q-canonical commutation relations (q-CCR), which is generated by a1, … , an subject to the relations ai∗aj=δij1+qajai∗.It has a distinguished representation πF called the Fock representation, which is believed to be faithful. In this article we denote the image of the universal enveloping C∗-algebra of q-CCR in the Fock representation by ℶn,q. The question whether C∗-isomorphism ℶn,q≃ ℶn, holds has been considered in the literature and proved for | q| < 0.44. In this article we show that ℶn,q≃ ℶn, for | q| < 1.

Author

Oleksii Kuzmin

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Communications in Mathematical Physics

0010-3616 (ISSN) 1432-0916 (eISSN)

Vol. 399 3 1623-1645

Subject Categories (SSIF 2011)

Algebra and Logic

Geometry

DOI

10.1007/s00220-022-04580-x

More information

Latest update

7/5/2023 1