相关论文: Generalized Derivations and Rota-Baxter Operators …

The purpose of this paper is to study the relationships between a Hom-Lie superalgebra and its induced 3-ary-Hom-Lie superalgebra. We provide an overview of the theory and explore the structure properties such as ideals, center, derived…

In this paper, we first define twisted Rota-Baxter family operators on Hom-associative algebras indexed by a semigroup $\Omega$. Then we introduce and study Hom-NS-family algebras as the underlying structures of twisted Rota-Baxter family…

Reductions for systems of ODEs integrable via the standard factorization method (the Adler-Kostant-Symes scheme) or the generalized factorization method, developed by the authors earlier, are considered. Relationships between such…

The principal objective of this paper is to determine the structure of $n$-Lie derivations ($n\geq 3$) on generalized matrix algebras.It is shown that under certain mild assumptions, every $n$-Lie derivation can be decomposed into the sum…

This paper establishes a uniform procedure to split the operations in any algebraic operad, generalizing previous known notions of splitting algebraic structures from the dendriform algebra of Loday that splits the associative operation to…

In this paper, we introduce the notion of generalized representation of a $3$-Lie algebra, by which we obtain a generalized semidirect product $3$-Lie algebra. Moreover, we develop the corresponding cohomology theory. Various examples of…

We introduce the concept of {sigma, tau}-Rota-Baxter operator, as a twisted version of a Rota-Baxter operator of weight zero. We show how to obtain a certain {sigma, tau}-Rota-Baxter operator from a solution of the associative…

It is shown that generalized Rota-Baxter operators introduced in [W.A. Martinez, E.G. Reyes & M. Ronco, Int. J. Geom. Meth. Mod. Phys. 18 (2021) 2150176] are a special case of Rota-Baxter systems [T. Brzezi\'nski, J. Algebra 460 (2016),…

This paper is devoted to studying deformation, cohomology theory of Rota-Baxter pre-Lie algebras of arbitrary weights. First we give the notion of a new representation of a Rota-Baxter pre-Lie algebra of arbitrary weight and define the…

Hom-Lie algebras are non-associative algebras generalizing Lie algebras by twisting the Jacobi identity by an endomorphism. The main examples are algebras of twisted derivations (i.e., linear maps with a generalized Leibniz rule). Such…

We generalize to arbitrary categories of algebras the notion of an NS-algebra. We do this by using a bimodule property, as we did for defining the general notions of a dendriform and tridendriform algebra. We show that several types of…

The notion of $\mathcal{O}$-operators on modules over Lie algebras generalize Rota-Baxter operators. They also generalize Poisson structures on Lie algebras in the presence of modules. Motivated from Poisson structures, we define gauge…

Hom-Lie superalgebras, which can be considered as a deformation of Lie superalgebras, are $\mathbb{Z}_2$-graded generalization of Hom-Lie algebras. In this paper, we prove that there is only the trivial Hom-Lie superalgebra structure over a…

Rota-Baxter systems were introduced by Brzezi\'{n}ski as a generalization of Rota-Baxter operators that are related to dendriform structures, associative Yang-Baxter pairs and covariant bialgebras. In this paper, we define Rota-Baxter…

Rota-Baxter systems of T. Brzezi\'{n}ski are a generalization of Rota-Baxter operators that are related to dendriform structures, associative Yang-Baxter pairs and covariant bialgebras. In this paper, we consider Rota-Baxter systems in the…

In this paper, we define generalized Casimir operators for a loop contragredient Lie superalgebra and prove that they commute with the underlying Lie superalgebra. These operators have applications in the decomposition of tensor product…

First we use a new approach to give a graded Lie algebra whose Maurer-Cartan elements characterize pre-Lie algebra structures. Then using this graded Lie bracket we define the notion of a Nijenhuis operator on a pre-Lie algebra which…

We introduce a notion of $n$-Lie Rinehart algebras as a generalization of Lie Rinehart algebras to $n$-ary case. This notion is also an algebraic analogue of $n$-Lie algebroids. We develop representation theory and describe a cohomology…

In this paper, using extension theory and cohomological approach we introduce the notion of the obstruction class for an inner post-Lie algebra being induced by a Rota-Baxter operator, and show that an inner post-Lie algebra is induced by a…

In this paper, first we introduce the notion of a twisted Rota-Baxter operator on a 3-Lie algebra $\g$ with a representation on $V$. We show that a twisted Rota-Baxter operator induces a 3-Lie algebra structure on $V$, which represents on…