Related papers: The Rota-Baxter algebra structures on split semi-q…
In this brief note we would like to report on an observation concerning the relation between Rota-Baxter operators and Loday-type algebras, i.e. dendriform di- and trialgebras. It is shown that associative algebras equipped with a…
We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and…
In this paper we study $k$-order homogeneous Rota-Baxter operators with weight $1$ on the simple $3$-Lie algebra $A_{\omega}$ (over a field of characteristic zero), which is realized by an associative commutative algebra $A$ and a…
In this paper, we introduce two types of deformation maps of quasi-twilled associative algebras. Each type of deformation maps unify various operators on associative algebras. Right deformation maps unify modified Rota-Baxter operators of…
In this paper, we propose the concept of an $\Omega$-Rota-Baxter system, which is a generalization of a Rota-Baxter system and an $\Omega$-Rota-Baxter algebra of weight zero. In the framework of operated algebras, we obtain a linear basis…
We characterise algebras commutative with respect to a Yang-Baxter operator (quasi-commutative algebras) in terms of certain cosimplicial complexes. In some cases this characterisation allows the classification of all possible…
Representations and relative Rota-Baxter operators with respect to representations of Hom-Leibniz Poisson algebras are introduced and studied. Some characterizations of these operators are obtained. The notion of matched pair and Nijenhuis…
We define and derive basic properties of the notion of Rota-Baxter operator on anti-flexible algebra. Starting from a Rota-Baxter operator on an anti-flexible algebra, we construct pre-anti-flexible algebra structure and associated…
Differential operators and integral operators are linked together by the first fundamental theorem of calculus. Based on this principle, the notion of a differential Rota-Baxter algebra was proposed by Guo and Keigher from an algebraic…
Rota-Baxter operators and more generally $\mathcal{O}$-operators play a crucial role in broad areas of mathematics and physics, such as integrable systems, the Yang-Baxter equation and pre-Lie algebras. The main objects of study in the…
We propose the notion of Hopf module algebras and show that the projection onto the subspace of coinvariants is an idempotent Rota-Baxter operator of weight -1. We also provide a construction of Hopf module algebras by using Yetter-Drinfeld…
We introduce the notion of quasi-triangular Leibniz bialgebras, which can be constructed from solutions of the classical Leibniz Yang-Baxter equation (CLYBE) whose skew-symmetric parts are invariant. In addition to triangular Leibniz…
This paper studies Rota-Baxter, Reynolds, Nijenhuis, and Averaging operators on 2-dimensional pre-Lie algebras over $\mathbb{C}$. Using the classification of 2-dimensional pre-Lie algebras and computational tools like Mathematica or Maple,…
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…
We describe Rota-Baxter operators, Reynolds operators, Nijenhuis operators, and Averaging operators on 2-dimensional dendriform algebras over $\mathbb{C}$.
We classify all Rota-Baxter operators on the simple conformal Lie algebra $\mathrm{Cur}(\mathrm{sl}_2(\mathbb{C}))$ and clarify which of them arise from the solutions to the conformal classical Yang-Baxter equation due to the connection…
We construct Baxter operators for the homogeneous closed $\mathrm{XXX}$ spin chain with the quantum space carrying infinite or finite dimensional $s\ell_2$ representations. All algebraic relations of Baxter operators and transfer matrices…
We will introduce an associative (or quantum) version of Poisson structure tensors. This object is defined as an operator satisfying a "generalized" Rota-Baxter identity of weight zero. Such operators are called generalized Rota-Baxter…
In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved.…
In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This…