Journal of Lie Theory

no. 2
Polynomial Modules over a Class of GIM Lie Algebras
Journal of Lie Theory, Volume 34 (2024) no. 2, pp. 481-501

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.

Received:
Revised:
Accepted:
DOI: 10.5802/jolt.1345 
@article{JOLT_2024_34_2_a10,
     author = {L. Xia and H. Yang},
     title = {Polynomial {Modules} over a {Class} of {GIM} {Lie} {Algebras
}},
     journal = {Journal of Lie Theory},
     pages = {481--501},
     year = {2024},
     volume = {34},
     number = {2},
     doi = {10.5802/jolt.1345},
     zbl = {1552.17007},
     language = {en},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1345/}
}
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%A L. Xia
%A H. Yang
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%J Journal of Lie Theory
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L. Xia; H. Yang. Polynomial Modules over a Class of GIM Lie Algebras. Journal of Lie Theory, Volume 34 (2024) no. 2, pp. 481-501. doi: 10.5802/jolt.1345

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