Journal of Lie Theory

no. 4
Representations of Simple Hom-Lie Algebras
Journal of Lie Theory, Volume 29 (2019) no. 4, pp. 1119-1135
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.
DOI: 10.5802/jolt.1096
Classification: 17B10, 17B15, 17B20
Keywords: Hom-Lie algebra, simple Hom-Lie algebra, representation, weight module 
@article{JOLT_2019_29_4_a13,
     author = {B. Agrebaoui and K. Benali and A. Makhlouf},
     title = {Representations of {Simple} {Hom-Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {1119--1135},
     year = {2019},
     volume = {29},
     number = {4},
     doi = {10.5802/jolt.1096},
     zbl = {1436.17010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1096/}
}
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B. Agrebaoui; K. Benali; A. Makhlouf. Representations of Simple Hom-Lie Algebras. Journal of Lie Theory, Volume 29 (2019) no. 4, pp. 1119-1135. doi: 10.5802/jolt.1096

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