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arXiv · 1309.7544

The irreducible modules for the derivations of the rational quantum torus

S. Eswara Rao·Punita Batra·Sachin S. Sharma
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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 $1 \leq i, j \leq d.$ 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 $gl_d$-module.

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S. Eswara Rao, Punita Batra, Sachin S. Sharma. 2015-01-28. The irreducible modules for the derivations of the rational quantum torus. https://doi.org/10.1016/j.jalgebra.2014.03.024

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