Representations of Simple Hom-Lie algebras

2019/03/21 by Agrebaoui, Boujemaa, Benali, Karima, Makhlouf, Abdenacer
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1903.08874

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 \mathfraksl₂-type Hom-Lie algebras.

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