Geodesic
Representations of Simple Hom-Lie Algebras
Boujemaa Agrebaoui1 ; Karima Benali1, 2 ; Abdenacer Makhlouf2
1Université de Sfax, Dép. des Mathématiques, Sfax 3038, Tunisia
2Université de Haute Alsace, IRIMAS -- Dép. des Mathématiques, 68093 Mulhouse, France
Journal of Lie Theory, Tome 29 (2019) no. 4, pp. 1119-1135

Voir la notice de l'article provenant de la source Heldermann Verlag

The purpose of this paper is to study representations of simple multiplicative Hom-Lie algebras. First, we provide a new proof using Killing form for the characterization theorem of simple Hom-Lie algebras given by Chen and Han, then discuss the representations structure of simple multiplicative Hom-Lie algebras. Moreover, we study weight modules and root space decompositions of simple multiplicative Hom-Lie algebras, characterize weight modules and provide examples of representations of sl2-type Hom-Lie algebras.
Classification : 17B10, 17B15, 17B20
Mots-clés : Hom-Lie algebra, simple Hom-Lie algebra, representation, weight module

Boujemaa Agrebaoui  1   ; Karima Benali  1 , 2   ; Abdenacer Makhlouf  2

1 Université de Sfax, Dép. des Mathématiques, Sfax 3038, Tunisia
2 Université de Haute Alsace, IRIMAS -- Dép. des Mathématiques, 68093 Mulhouse, France 
Boujemaa Agrebaoui; Karima Benali; Abdenacer Makhlouf. Representations of Simple Hom-Lie Algebras. Journal of Lie Theory, Tome 29 (2019) no. 4, pp. 1119-1135. http://geodesic.mathdoc.fr/item/JOLT_2019_29_4_a13/
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     author = {Boujemaa Agrebaoui and Karima Benali and Abdenacer Makhlouf},
     title = {Representations of {Simple} {Hom-Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {1119--1135},
     year = {2019},
     volume = {29},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2019_29_4_a13/}
}
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