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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


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