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math.RA2025
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…
math.RA2025
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…
math.RA2024
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…