5 papers
On formal deformations and degenerations of evolution algebras
Abdenacer Makhlouf, Andrés Pérez-RodrÃguez
The main purpose of this paper is to study formal deformations of evolution algebras, determining their existence and classifying them up to equivalence. In addition, we examine de…
The Superization of Hochschild's Lemma and Restricted Lie-Rinehart Superalgebras
Sofiane Bouarroudj, Quentin Ehret, Abdenacer Makhlouf +1
The main goal of this paper is to introduce the notion of restricted Lie-Rinehart superalgebra over a field of characteristic , motivated by a generalization of Hochschild's l…
Curved O-operator systems
Tianshui Ma, Abdenacer Makhlouf, Sergei Silvestrov
In this paper, we introduce the notion of curved -operator systems as a generalization of T. BrzeziÅski's (curved) Rota-Baxter systems, and then investigate their rel…
Cohomology and deformations of restricted Lie algebras and their morphisms in positive characteristic
Quentin Ehret, Abdenacer Makhlouf
The main purpose of this paper is to study cohomology and develop a deformation theory of restricted Lie algebras in positive characteristic . In the case , it is show…
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…