Irreducible modules over the divergence zero algebras and their $q$-analogues

Xuewen Liu; Xiangqian Guo; Zhen Wei

Irreducible modules over the divergence zero algebras and their $q$-analogues

Representation Theory 2017-09-12 v1

Authors: Xuewen Liu , Xiangqian Guo , Zhen Wei

Abstract

In this paper, we study a class of $\Z_d$ -graded modules, which are constructed using Larsson's functor from $\sl_d$ -modules $V$ , for the Lie algebras of divergence zero vector fields on tori and quantum tori. We determine the irreducibility of these modules for finite-dimensional or infinite-dimensional $V$ using a unified method. In particular, these modules provide new irreducible weight modules with infinite-dimensional weight spaces for the corresponding algebras.

Keywords

divergence zero algebras q-analogues irreducible modules graded modules Larsson's functor Lie algebras weight modules

Cite

@article{arxiv.1709.02972,
  title  = {Irreducible modules over the divergence zero algebras and their $q$-analogues},
  author = {Xuewen Liu and Xiangqian Guo and Zhen Wei},
  journal= {arXiv preprint arXiv:1709.02972},
  year   = {2017}
}

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