Resumen de Generalized representations of 3-Hom-Lie algebra

S. Mabrouk, A. Makhlouf, S. Massoud

• 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