arXiv subjects

O. Ncib

Publications and source records attributed to O. Ncib.

5 recordsLinked to original sources

arXiv2026

Hom-Poisson superalgebras with nondegenerate bilinear forms and compatible Hom-anti-pre-Poisson superalgebras

In this paper, we first introduce the notions of Hom-anti-Zinbiel superalgebras, extending the corresponding anti-algebraic structures to the Hom-super setting. We develop their fundamental properties and characterize them in terms of anti-super-$\mathcal O$-operators and anti-Rota-Baxter operators. Furthermore, we introduce the concepts of super-commutative Connes cocycles on super-commutative Hom-associative superalgebras and super-commutative $2$-cocycles on Hom-Lie superalgebras. We prove that nondegenerate super-commutative Connes cocycles give rise to compatible Hom-anti-Zinbiel superalgebra structures, while nondegenerate super-commutative $2$-cocycles induce compatible Hom-anti-pre-Lie superalgebra structures. As a main application, we show that a Hom-Poisson superalgebra equipped with a nondegenerate super-commutative Connes cocycle on its Hom-associative component and a nondegenerate super-commutative $2$-cocycle on its Hom-Lie component canonically determines a compatible Hom-anti-pre-Poisson superalgebra, and conversely. This provides a unified framework linking Hom-Poisson and Hom-anti-pre-Poisson superalgebras and reveals the fundamental role played by nondegenerate supersymmetric bilinear forms in the structure theory of Hom-type superalgebras. Several further structural results and characterizations are also obtained.

math.RA↗

arXiv2026

On noncommutative Hom-anti-pre-Poisson superalgebras and related structures

In this paper, we develop the theory of several Hom-type anti-algebraic structures in the $\mathbb{Z}_2$-graded setting. We introduce and study Hom-anti-associative superalgebras, Hom-anti-dendriform superalgebras, and Hom-anti-pre-Lie superalgebras, which arise as Hom-type generalizations of the corresponding anti-algebraic structures. Various constructions and examples are provided, together with structural properties and representation-theoretic aspects. In particular, we investigate the role of anti-super-$\mathcal{O}$-operators and anti-Rota-Baxter operators in the construction of Hom-anti-dendriform superalgebras. Furthermore, we introduce the notion of noncommutative Hom-pre-Poisson superalgebras and noncommutative Hom-anti-pre-Poisson superalgebras as Hom-type extensions of noncommutative Poisson-type structures in the graded framework. These structures naturally combine Hom-anti-pre-Lie and Hom-anti-dendriform superalgebras through suitable compatibility conditions. Several relationships between the introduced structures are established, providing a unified framework for studying twisted and graded generalizations of noncommutative Poisson-type algebras.

math.RA↗

arXiv2023

Pseudo-Euclidean Hom-alternative superalgebras and Hom-post-alternative superalgebras

The purpose of this paper is to study pseudo-Euclidean and symplectic Hom-alternative superalgebras and discuss some of their proprieties and provide construction procedures. We also introduce the notion of Rota-Baxter operators of pseudo-Euclidean Hom-alternative superalgebras of any weight and Hom-post-alternative superalgebras. A Hom-post-alternative superalgebras consists of three operations such that some compatibility conditions are satisfied. We show that a weighted Rota-Baxter operator induces a Hom-post-alternative superalgebra naturally. Conversely, a Hom-post-alternative superalgebra gives rise to a new Hom-alternative superalgebra. In particular, a Hom-pre-alternative superalgebra is naturally built via symplectic structures.

math.RA↗

arXiv2022

Malcev Yang-Baxter equation, weighted $\mathcal{O}$-operators on Malcev algebras and post-Malcev algebras

The purpose of this paper is to study the $\mathcal{O}$-operators on Malcev algebras and discuss the solutions of Malcev Yang-Baxter equation by $\mathcal{O}$-operators. Furthermore we introduce the notion of weighted $\mathcal{O}$-operators on Malcev algebras, which can be characterized by graphs of the semi-direct product Malcev algebra. Then we introduce a new algebraic structure called post-Malcev algebras. Therefore, post-Malcev algebras can be viewed as the underlying algebraic structures of weighted $\mathcal{O}$-operators on Malcev algebras. A post-Malcev algebra also gives rise to a new Malcev algebra. Post-Malcev algebras are analogues for Malcev algebras of post-Lie algebras and fit into a bigger framework with a close relationship with post-alternative algebras.

math.RA↗

arXiv2022

Dendrification of Hom-Malcev algebras

The main goal of this work is to introduce the notion of Hom-M-dendriform algebras which are the dendriform version of Hom-Malcev algebras. In fact they are the algebraic structures behind the $\mathcal{O}$-operator of Hom-pre-Malcev algebras. They also fit into a bigger framework as Hom-Malcev algebraic analogues of Hom-L-dendriform algebras. Furthermore, we show a connections between Hom-M-Dendriform algebras and Hom-alternative quadri-algebras.

math.RA↗