The irreducible modules for the derivations of the rational quantum torus

الأصل · EN

Let be the quantum torus associated with the d × d matrix q = (qij), qii = 1, qij⁻¹ = qji, qij are roots of unity, for all 1 ≤ i, j ≤ d. Let () be the Lie algebra of all the derivations of. In this paper we define the Lie algebra () and classify its modules which are irreducible and have finite dimensional weight spaces. These modules under certain conditions turn out to be of the form V ⊗, where V is a finite dimensional irreducible gld-module.