8 papers
Splitting of operations for Hom-diassociative and Hom-triassociative Algebras
Abdelkader Hamdouni, Imed Basdouri, Mariem Jendoubi +1
Hom-quadri dendriform algebras and Hom-six-dendriform agebras are introduced and studied which is a splitting of a Hom-diassociative and Hom-triassociative algebras, respectively.…
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…
Related Hom-rhizaform algebras and Rota-Baxter Operators, Hom-Rhizaform Family Algebras
Imed Basdouri, Mariem Jendoubi, Ahmed Zahari Abdou Damdji
This paper explores the link between Hom-rhizaform algebras and Rota-Baxter operators. We define a new structure, the Hom-rhizaform family algebra, which is a more general version…
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…