Journal of Lie Theory 29 (2019), No. 4, 1119--1135
Copyright Heldermann Verlag 2019
Representations of Simple Hom-Lie Algebras
Boujemaa Agrebaoui
Université de Sfax, Dép. des Mathématiques, Sfax 3038, Tunisia
b.agreba@fss.rnu.tn
Karima Benali
Université de Sfax, Dép. des Mathématiques, Sfax 3038, Tunisia
and: Université de Haute Alsace, IRIMAS -- Dép. des Mathématiques, 68093 Mulhouse, France
karimabenali172@yahoo.fr
Abdenacer Makhlouf
Université de Haute Alsace, IRIMAS -- Dép. des Mathématiques, 68093 Mulhouse, France
abdenacer.makhlouf@uha.fr
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.
Keywords: Hom-Lie algebra, simple Hom-Lie algebra, representation, weight module.
MSC: 17B10, 17B15, 17B20.
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