Generalized representations of 3-Hom-Lie algebras

Authors

  • S. Mabrouk University of Gafsa, Faculty of Sciences Gafsa, 2112 Gafsa, Tunisia
  • A. Makhlouf Université de Haute Alsace, IRIMAS-département de Mathématiques
  • S. Massoud Université de Sfax, Faculté des Sciences, Sfax Tunisia

DOI:

https://doi.org/10.17398/2605-5686.35.1.99

Keywords:

3-Hom-Lie algebra, representation, generalized representation, cohomology, Abelian extension

Abstract

The propose of this paper is to extend generalized representations of 3-Lie algebras to Hom-type algebras. We introduce the concept of generalized representation of multiplicative 3-Hom-Lie algebras, develop the corresponding cohomology theory and study semi-direct products. We provide a key construction, various examples and computation of 2-cocycles of the new cohomology. Also, we give a connection between a split abelian extension of a 3-Hom-Lie algebra and a generalized semidirect product 3-Hom-Lie algebra.

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Published

2020-06-01

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Section

Non-associative Rings and Algebras

How to Cite

Generalized representations of 3-Hom-Lie algebras. (2020). Extracta Mathematicae, 35(1), 99-126. https://doi.org/10.17398/2605-5686.35.1.99

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