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

2017/09/09 by Xuewen Liu, Xiangqian Guo, Liu, Xuewen +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1709.02972

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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• Tensor modules over the Lie algebras of divergence zero vector fields on ℂⁿ

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