Irreducible modules over the derivation algebras of rational quantum tori (Q661877)

In this paper the authors study certain uniformly bounded weight modules over the Lie algebra of derivations of a rational quantum torus constructed in [\textit{W. Li} and \textit{S. Tan}, J. Algebra 275, No. 1, 250--274 (2004; Zbl 1106.17020)]. This family originally depended on two parameters, a choice of a \(\mathfrak{gl}_n\)-module and a group homomorphism from \(\mathbb{Z}^n\) to \(\mathbb{C}^*\). In the present paper the authors show that the second parameter is redundant up to isomorphism which allows them to restrict the study to a very special case of ``easy'' homomorphisms and use this to give a very transparent description of modules and their properties, including an irreducibility criterion and an isomorphism criterion.