Representations of a Class of Non-commutative Associative Algebras Related to the Quantum Torus

Abstract

In this paper, we study the representations of a class of non-commutative associative algebras AQ related to the quantum torus [Formula: see text], which is introduced by Berman, Gao and Krylyuk to study the extended affine Lie algebras. The representations of AQ are important for the study of the representations of certain “half lattice” vertex algebras.