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

Combining the notions of braces and relative Rota-Baxter operators on groups in connection with the Yang-Baxter equation and a factorization theorem of Lie groups from integrable systems, relative Rota-Baxter operators on braces and…

We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative…

The homogeneous Rota-Baxter operators on the Witt and Virasoro algebras are classified. As applications, the induced solutions of the classical Yang-Baxter equation and the induced pre-Lie and PostLie algebra structures are obtained.

In this paper, we introduce the notion of modified Rota-Baxter operators of non-zero weight on $3$-Lie algebras and provide some examples. Next, we give various constructions of modified Rota-Baxter operators of non-zero weight according to…

This paper introduces Hom-type analogues of affine algebraic structures, termed Hom-affgebras. Extending Brzezi\'nski's theory of affgebras and the Hom-algebra framework developed by Hartwig-Larsson-Silvestrov, we define and study…

The aim of this paper is to introduce the notion of restricted Hom- Lie superalgebras. This class of algebras is a generalization of both restricted Hom-Lie algebras and restricted Lie superalgebras. In this paper, we present a way to…

In the present paper, we define the new class of representation on $n$-Lie algebra that is called as generalized representation. We study the cohomology theory corresponding to generalized representations of $n$-Lie algebras and show its…

At the previous congress (CRM 6), we reviewed the construction of Yang-Baxter operators from associative algebras, and presented some (colored) bialgebras and Yang-Baxter systems related to them. The current talk deals with Yang-Baxter…

In the paper, we introduce the notion of a Rota-Baxter operator of a non-scalar weight. As a motivation, we show that there is a natural connection between Rota-Baxter operators of this type and structures of quasitriangular Lie bialgebras…

Rota--Baxter operators $R$ of weight $1$ on $\mathfrak{n}$ are in bijective correspondence to post-Lie algebra structures on pairs $(\mathfrak{g},\mathfrak{n})$, where $\mathfrak{n}$ is complete. We use such Rota--Baxter operators to study…

A twisted generalization of Lie-Yamaguti algebras, called Hom-Lie-Yamaguti algebras, is defined. Hom-Lie-Yamaguti algebras generalize Hom-Lie triple systems (and susequently ternary Hom-Nambu algebras) and Hom-Lie algebras in the same way…

The notion of $n$-ary algebras, that is vector spaces with a multiplication concerning $n$-arguments, $n \geq 3$, became fundamental since the works of Nambu. Here we first present general notions concerning $n$-ary algebras and associative…

In this paper, first we introduce the notion of a post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and there is naturally a post-Hopf algebra structure on the universal enveloping algebra of a…

In this paper, first we revisit the formal integration of Lie algebras, which give rise to braces in some special cases. Then we establish the formal integration theory for complete Rota-Baxter Lie algebras, that is, we show that there is a…

Motivated by recent work on Hom-Lie algebras and the Hom-Yang-Baxter equation, we introduce a twisted generalization of the classical Yang-Baxter equation (CYBE), called the classical Hom-Yang-Baxter equation (CHYBE). We show how an…

The purpose of this paper is to discuss the universal algebra theory of hom-algebras. This kind of algebra involves a linear map which twists the usual identities. We focus on hom-associative algebras and hom-Lie algebras for which we…

In this paper, we define representations and cohomology of weighted Rota-Baxter Lie algebras. As applications of cohomology, we study abelian extensions and formal $1$-parameter deformations weighted Rota-Baxter Lie algebras. Finally, we…

A cohomology theory of weighted Rota-Baxter $3$-Lie algebras is introduced. Formal deformations, abelian extensions, skeletal weighted Rota-Baxter $3$-Lie 2-algebras and crossed modules of weighted Rota-Baxter 3-Lie algebras are interpreted…

In this paper, we introduce the notion of Rota-Baxter Lie $2$-algebras, which is a categorification of Rota-Baxter Lie algebras. We prove that the category of Rota-Baxter Lie $2$-algebras and the category of $2$-term Rota-Baxter…

A class of non-associative and non-coassociative generalizations of cobraided bialgebras, called cobraided Hom-bialgebras, is introduced. The non-(co)associativity in a cobraided Hom-bialgebra is controlled by a twisting map. Several…