The irreducible modules for the derivations of the rational quantum torus

Abstract

Let $\bbcq$ be the quantum torus associated with the $d\times d$ matrix $q=(q_{ij})$, $q_{ii}=1$, $q_{ij}^{-1}=q_{ji}$, $q_{ij}$ are roots of unity, for all $1\le i,j\le d.$ Let $\Der(\bbcq)$ be the Lie algebra of all the derivations of $\bbcq$. In this paper we define the Lie algebra $\Der(\bbcq) \ltimes \bbcq$ 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 $V \otimes \bbcq$, where $V$ is a finite dimensional irreducible $g{l}_d$-module.

Revised version

Cited by in corpus (1)

• Cuspidal modules for the derivation Lie algebra over a rational quantum torus