12 papers
Cohomology and deformation theory of Reynolds--Nijenhuis associative algebras
Bouzid Mosbahi, Imed Basdouri, Jean Lerbet
In this paper, we introduce and study Reynolds--Nijenhuis operators on associative algebras a novel hybrid structure that simultaneously satisfies the defining identities of both R…
Hochschild cohomology groups of 5-dimensional complex nilpotent associative algebras
Bouzid Mosbahi, Imed Basdouri, Jean Lerbet
This paper explores the structure of low-dimensional cohomology groups in the context of complex nilpotent associative algebras. Specifically, we study 5-dimensional complex nilpot…
Cohomology and deformation theory of Averaging Leibniz algebras
Bouzid Mosbahi, Imed Basdouri, Jean Lerbet
In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additiona…
Compatible Pairs of Low-Dimensional Associative Algebras and Their Invariants
Ahmed Zahari Abdou Damdji, Bouzid Mosbahi
A compatible associative algebra is a vector space endowed with two associative multiplication operations that satisfy a natural compatibility condition. In this paper, we investig…
Rota-Type Operators on 2-Dimensional Pre-Lie Algebras
Imed Basdouri, Bouzid Mosbahi, Ahmed Zahari
This paper studies Rota-Baxter, Reynolds, Nijenhuis, and Averaging operators on 2-dimensional pre-Lie algebras over . Using the classification of 2-dimensional pre-Lie…
Matrix Representations of Derivations for Low-Dimensional Mock-Lie Algebras
Imed Basdouri, Bouzid Mosbahi
In this work, we study the matrix representation of derivations for Mock-Lie algebras with dimensions up to four. Using matrix methods, we examine their structure and properties, s…