Stability of a Special Class of $$q_{ij}$$ -CCR and Extensions of Higher-Dimensional Noncommutative Tori

The -algebras A_{qi}, generated by generalised quon commutation relations are considered. The nuclearity of these algebras is proved. It is shown that A_{qi}, is isomorphic to the extension of a higher-dimensional noncommutative torus. Irreducible representations of A_{qi}, are considered. It is shown that the Fock representation is faithful.