Journal of Lie Theory 34 (2024), No. 2, 481--501
Copyright Heldermann Verlag 2024
Polynomial Modules over a Class of GIM Lie Algebras
Limeng Xia
Institute of Applied System Analysis, Jiangsu University, Zhenjiang, P. R. China
xialimeng@ujs.edu.cn
Hengyun Yang
Dept. of Mathematics, Shanghai Maritime University, Shanghai, P. R. China
hyyang@shmtu.edu.cn
[Abstract-pdf]
We construct and classify all rank one polynomial modules over the GIM Lie algebra ${\mathfrak g}_n$ ($n\geq 3$) with structural matrix \[ \begin{bmatrix} 2 & -1 & & & 1 \\ -1 & 2 & -1 & & \\ &\ddots& \ddots&\ddots& \\ & & -1 & 2& -1 \\ 1 & & & -1& 2 \end{bmatrix} _{n\times n}. \] Moreover, the simplicity of these modules is studied.
Keywords: Lie algebra, Cartan subalgebra, polynomial module, non-weight module.
MSC: 17B10, 17B65, 17B67.
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