5 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…
Central derivations of low-dimensional Zinbiel algebras
Basdouri Imed, Jean Lerbet, Bouzid Mosbahi
The study of central derivations in low-dimensional algebraic structures is a crucial area of research in mathematics, with applications in understanding the internal symmetries an…
Quasi-Centroids and Quasi-Derivations of low-dimensional Zinbiel algebras
Basdouri Imed, Jean Lerbet, Bouzid Mosbahi
In this paper, we introduce the concepts of quasi-centroid and quasi-derivation for Zinbiel algebras. Utilizing the classification results of Zinbiel algebras established previousl…