Generalized representations of 3-Hom-Lie algebra

• S. Mabrouk ^[1] ; A. Makhlouf ^[3] ; S. Massoud ^[2]
  1. [1] University of Gafsa

     University of Gafsa

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  2. [2] University of Sfax

     University of Sfax

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  3. [3] Universite de Haute Alsace, IRIMAS-departement de Mathematiques 6, rue des Fr`eres Lumi`ere F-68093 Mulhouse, Franc

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• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 35, Nº 1, 2020, págs. 99-126
• Idioma: inglés
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• Resumen

  • 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