arXiv subjects

Sonia Massoud

Publications and source records attributed to Sonia Massoud.

2 recordsLinked to original sources

arXiv2020

Constructions and representation theory of BiHom-post-Lie algebras

The main goal of this paper is to give some construction results of BiHom-post-Lie algebras which are a generalization of both post-Lie-algebras and Hom-post-Lie algebras. They are the algebraic structures behind the $\mathcal{O}$-operator of BiHom-Lie algebras. They can be also regarded as the splitting into three parts of the structure of a BiHom-Lie-algebra. Moreover we develop the representation theory of BiHom-post-Lie algebras on a vector space $V$. We show that there is naturally an induced representation of its sub-adjacent Lie algebra.

math.RA↗

arXiv2019

Generalized representations of 3-Hom-Lie algebras

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.

math.RT↗