Related papers: Rota-Baxter Operators on Quadratic Algebras
The all Rota-Baxter algebra structures on the polynomial algebra $R={\bf k}[x]$ are well known. We study the finite dimensional modules of polynomial Rota-Baxter algebras $(\bfk[x],P)$ or $(x {\bf k} [x],P)$ of weight nonzero since some…
In this paper, we introduce the notions of quasi-triangular and factorizable dendriform D-bialgebras. A factorizable dendriform D-bialgebra leads to a factorization of the underlying dendriform algebra. We show that the dendriform double of…
We introduce the concept of an extended O-operator that generalizes the well-known concept of a Rota-Baxter operator. We study the associative products coming from these operators and establish the relationship between extended O-operators…
In this paper, we introduce twisted relative Rota-Baxter operators on a Leibniz algebra as a generalization of twisted Poisson structures. We define the cohomology of a twisted relative Rota-Baxter operator $K$ as the Loday-Pirashvili…
In this paper, we introduce the notions of quasi-triangular and factorizable perm bialgebras, based on notions of the perm Yang-Baxter equation and $(R, \mathrm{ad})$-invariant condition. A factorizable perm bialgebra induces a…
We consider a complete filtered Rota-Baxter algebra of weight $\lambda$ over a commutative ring. Finding the unique solution of a non-homogeneous linear algebraic equation in this algebra, we generalize Spitzer's identity in both…
Theory of Rota-Baxter operators on rings and algebras has been developed since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined the notion of Rota-Baxter operator on a group. We provide some general constructions of…
The aim of this paper is to introduce and study the concepts of the Rota-Baxter operator and Reynolds operator within the framework of trusses. Moreover, we introduce and discuss dendriform trusses, tridendriform trusses, and NS-trusses as…
This paper investigates Rota-Baxter associative algebras of of arbitrary weights, that is, associative algebras endowed with Rota-Baxter operators of arbitrary weights from an operadic viewpoint. Denote by $\RB$ the operad of Rota-Baxter…
Rota--Baxter operators over groups have been recently defined in \cite{LHY2021}, and they share a close connection with skew braces, as demonstrated in \cite{VV2022}. In this paper, we classify all Rota--Baxter operators of weight 1 over…
In this letter, we use quantum quasi-shuffle algebras to construct Rota-Baxter algebras, as well as tridendriform algebras. We also propose the notion of braided Rota-Baxter algebras, which is the relevant object of Rota-Baxter algebras in…
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…
Representations of Hom-Jacobi-Jordan algebras are studied. In particular, adjoint representations and trivial representations are studied in detail. Derivations and central extensions of Hom-Jacobi-Jordan algebras are also discussed as an…
A commutative Rota-Baxter algebra can be regarded as a commutative algebra that carries an abstraction of the integral operator. With the motivation of generalizing the study of algebraic geometry to Rota-Baxter algebra, we extend 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 anti-dendriform bialgebras, which can be induced by the solutions of the AD-YBE whose symmetric parts are invariant. A factorizable anti-dendriform bialgebra leads to a factorization of the…
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…
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 consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra U_q(gl(M|N)^). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of U_q(gl(M|N)) in the…
A relative Rota-Baxter operator on Lie 2-groups is introduced as a pair of relative Rota-Baxter operators on the underlying Lie groups which is also a Lie groupoid morphism. Such an operator induces a factorization theorem for Lie 2-groups…