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40 papers · 1 filter
The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
Hani Abdelwahab, Ivan Kaygorodov, Abdenacer Makhlouf
In this paper, we develop a method to obtain the algebraic classification of compatible pre-Lie algebras from the classification of pre-Lie algebras of the same dimension. We use t…
(Non-BiHom-Commutative) BiHom-Poisson algebras
Hadjer Adimi, Hanene Amri, Sami Mabrouk +1
The aim of this paper is to introduce and study BiHom-Poisson algebras, in particular Non-BiHom-Commutative BiHom-Poisson algebras. We discuss their representation theory and Semi-…
Tensor products and perturbations of BiHom-Novikov-Poisson algebras
Ling Liu, Abdenacer Makhlouf, Claudia Menini +1
We study BiHom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras and Hom-Novikov-Poisson algebras, and find that BiHom-Novikov-Poisson algebra…
Ado theorem for nilpotent Hom-Lie algebras
Abdenacer Makhlouf, Pasha Zusmanovich
We prove an analog of the Ado theorem - the existence of a finite-dimensional faithful representation - for a certain kind of finite-dimensional nilpotent Hom-Lie algebras.
-type Hochschild cohomology of Hom-associative algebras and Hom-bialgebras
Benedikt Hurle, Abdenacer Makhlouf
In this paper we define a new cohomology for multiplicative Hom-associative algebras, which generalize Hochschild cohomology and fits with deformations of Hom-associative algebras…
Coadjoint orbits of Lie algebras and Cartan class
Michel Goze, Elisabeth Remm
We study the coadjoint orbits of a Lie algebra in terms of Cartan class. In fact, the tangent space to a coadjoint orbit at the point corresponds to the charac…