Generalized representations of 3-Hom-Lie algebras

2019/05/29 by Sami Mabrouk, Mabrouk, Sami, Abdenacer Makhlouf +3
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1905.13048

openalex publication_date 2019/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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