Irreducible modules for the loop of derivations of rational quantum torus

Abstract

Let [Formula: see text] be a rational quantum torus associated with the matrix [Formula: see text]. Let [Formula: see text] be the Lie algebra of derivations of [Formula: see text]. In this paper, we consider the Lie algebra [Formula: see text], where [Formula: see text] is a commutative associative unital algebra over [Formula: see text] and classify its irreducible modules with finite-dimensional weight spaces.