Geodesic
Polynomial Modules over a Class of GIM Lie Algebras
Journal of Lie theory, Tome 34 (2024) no. 2, pp. 481-501
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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.
Classification : 17B10, 17B65, 17B67
Mots-clés : Lie algebra, Cartan subalgebra, polynomial module, non-weight module 
@article{JLT_2024_34_2_JLT_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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2024_34_2_JLT_2024_34_2_a10/}
}
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L. Xia; H. Yang. Polynomial Modules over a Class of GIM Lie Algebras. Journal of Lie theory, Tome 34 (2024) no. 2, pp. 481-501. http://geodesic.mathdoc.fr/item/JLT_2024_34_2_JLT_2024_34_2_a10/