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

Xuewen Liu; Xiangqian Guo; Zhen Wei

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arXiv · 1709.02972

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

Xuewen Liu·Xiangqian Guo·Zhen Wei

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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.

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BibTeX RIS

Xuewen Liu, Xiangqian Guo, Zhen Wei. 2017-09-09. Irreducible modules over the divergence zero algebras and their $q$-analogues. https://arxiv.org/abs/1709.02972

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