arXiv subjects

Sami Benabdelhafidh

Publications and source records attributed to Sami Benabdelhafidh.

4 recordsLinked to original sources

arXiv2025

Cohomology theory of Nijenhuis family $Ω$-associative algebras

Family algebraic structures indexed by a semigroup first appeared in the algebraic aspects of renormalizations in quantum field theory. In this paper, we first introduce the concept of Nijenhuis family $Ω$-associative algebras and we discuss the relationship between Nijenhuis family and other operators families on $Ω$-associative algebras. Then, we define the cohomology theory of Nijenhuis family $Ω$-associative algebras and show that this cohomology controls the corresponding deformations. Finally, we study abelian extensions of Nijenhuis family $Ω$-associative algebras in terms of the second cohomology group.

math.RA↗

arXiv2025

Deformations theory and minimal model of operads for Nijenhuis algebras morphisms

Nijenhuis operators are very useful in the deformation theory of algebras. In this paper, we introduce a new cohomology theory related to deformation of Nijenhuis algebra morphisms, this notion involves simultaneous deformation of two Nijenhuis algebras and a morphism between them. As a consequence, we define a cohomology theory of Nijenhuis algebra morphisms to interpret the lower degree cohomology groups as formal deformation. We also prove a cohomology comparison Theorem of Nijenhuis algebra morphisms, i.e. the cohomology of a morphism of Nijenhuis algebras is isomorphic to the cohomology of an auxiliary Nijenhuis algebra. Finally, we construct a minimal model for the operad governing Nijenhuis algebras morphisms.

math.RA↗

arXiv2024

A cohomological study of modified Rota-Baxter associative algebras with derivations

This paper presents a cohomological study of modified Rota-Baxter associative algebras in the presence of derivations. The Modified Rota-Baxter operator, which is a modified version and closely related to the classical Rota-Baxter operator, has garnered significant attention due to its applications in various mathematical and physical contexts. In this study, we define a cohomology theory and also investigate a one-parameter formal deformation theory and abelian extensions of modified Rota-Baxter associative algebras under the influence of derivations.

math.RA↗

arXiv2024

Cohomologies of modified Rota-Baxter Lie algebras with derivations and applications

In this paper, first, we introduce a notion of modified Rota-Baxter Lie algebras of weight $\mathrmλ$ with derivations (or simply modified Rota-Baxter LieDer pairs) and their representations. Moreover, we investigate cohomologies of a modified Rota-Baxter LieDer pairs with coefficients in a suitable representation. As applications, we study formal one-parameter deformations and abelian extensions of modified Rota-Baxter LieDer pairs.

math.RA↗