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arXiv · 1903.08874

Representations of Simple Hom-Lie algebras

Boujemaa Agrebaoui·Karima Benali·Abdenacer Makhlouf
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Abstract

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 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 $\mathfrak{sl}_2$-type Hom-Lie algebras.

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Boujemaa Agrebaoui, Karima Benali, Abdenacer Makhlouf. 2019-03-21. Representations of Simple Hom-Lie algebras. https://arxiv.org/abs/1903.08874

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