Graded modules over simple Lie algebras

Yuri Bahturin; Mikhail Kochetov; Abdallah Shihadeh

doi:10.15446/recolma.v53nsupl.84006

Publié-e

2019-12-11

Graded modules over simple Lie algebras

DOI :

https://doi.org/10.15446/recolma.v53nsupl.84006

Mots-clés :

graded Lie algebras, graded modules, simple modules, universal enveloping algebra (en)
Álgebras de Lie graduadas, módulos graduados, módulos simples, álgebra envolvente universal (es)

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Auteurs-es

Yuri Bahturin Memorial University of Newfoundland
Mikhail Kochetov Memorial University of Newfoundland
Abdallah Shihadeh Memorial University of Newfoundland

Résumé (en)
Résumé (es)

The paper is devoted to the study of graded-simple modules and gradings on simple modules over finite-dimensional simple Lie algebras. In general, a connection between these two objects is given by the so-called loop construction. We review the main features of this construction as well as necessary and sufficient conditions under which finite-dimensional simple modules can be graded. Over the Lie algebra sl₂(C), we consider specific gradings on simple modules of arbitrary dimension.

El artículo está dedicado al estudio de módulos graduados simples y graduaciones de módulos simples sobre álgebras de Lie simples de dimensión finita. En general, una conexión entre estos dos objetos viene dada por la llamada construcción de lazos. Revisaremos las características principales de esta construcción, así como las condiciones necesarias y suficientes bajo las cuales se pueden graduar los módulos simples de dimensión finita. Para el álgebra de Lie sl₂(C), consideramos graduaciones específicas en módulos simples de dimensión arbitraria.

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Comment citer

APA

Bahturin, Y., Kochetov, M. et Shihadeh, A. (2019). Graded modules over simple Lie algebras. Revista Colombiana de Matemáticas, 53(supl), 45–86. https://doi.org/10.15446/recolma.v53nsupl.84006

ACM

[1]

Bahturin, Y., Kochetov, M. et Shihadeh, A. 2019. Graded modules over simple Lie algebras. Revista Colombiana de Matemáticas. 53, supl (déc. 2019), 45–86. DOI:https://doi.org/10.15446/recolma.v53nsupl.84006.

ACS

(1)

Bahturin, Y.; Kochetov, M.; Shihadeh, A. Graded modules over simple Lie algebras. rev.colomb.mat 2019, 53, 45-86.

ABNT

BAHTURIN, Y.; KOCHETOV, M.; SHIHADEH, A. Graded modules over simple Lie algebras. Revista Colombiana de Matemáticas, [S. l.], v. 53, n. supl, p. 45–86, 2019. DOI: 10.15446/recolma.v53nsupl.84006. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/84006. Acesso em: 22 janv. 2025.

Chicago

Bahturin, Yuri, Mikhail Kochetov, et Abdallah Shihadeh. 2019. « Graded modules over simple Lie algebras ». Revista Colombiana De Matemáticas 53 (supl):45-86. https://doi.org/10.15446/recolma.v53nsupl.84006.

Harvard

Bahturin, Y., Kochetov, M. et Shihadeh, A. (2019) « Graded modules over simple Lie algebras », Revista Colombiana de Matemáticas, 53(supl), p. 45–86. doi: 10.15446/recolma.v53nsupl.84006.

IEEE

[1]

Y. Bahturin, M. Kochetov, et A. Shihadeh, « Graded modules over simple Lie algebras », rev.colomb.mat, vol. 53, nᵒ supl, p. 45–86, déc. 2019.

MLA

Bahturin, Y., M. Kochetov, et A. Shihadeh. « Graded modules over simple Lie algebras ». Revista Colombiana de Matemáticas, vol. 53, nᵒ supl, décembre 2019, p. 45-86, doi:10.15446/recolma.v53nsupl.84006.

Turabian

Bahturin, Yuri, Mikhail Kochetov, et Abdallah Shihadeh. « Graded modules over simple Lie algebras ». Revista Colombiana de Matemáticas 53, no. supl (décembre 11, 2019): 45–86. Consulté le janvier 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/84006.

Vancouver

1.

Bahturin Y, Kochetov M, Shihadeh A. Graded modules over simple Lie algebras. rev.colomb.mat [Internet]. 11 déc. 2019 [cité 22 janv. 2025];53(supl):45-86. Disponible à: https://revistas.unal.edu.co/index.php/recolma/article/view/84006

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CrossRef Cited-by

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1. Yuri Bahturin, Abdallah Shihadeh. (2022). Graded torsion-free 𝔰𝔩2(ℂ)-modules of rank 2. Journal of Algebra and Its Applications, 21(11) https://doi.org/10.1142/S0219498822502292.