相关论文: Modules of polynomial Rota-Baxter Algebras and mat…
In this paper, we obtain a canonical factorization of basis elements in free Rota-Baxter algebras built on bracketed words. This canonical factorization is applied to give a coalgebra structure on the free Rota-Baxter algebras. Together…
We describe all Rota-Baxter operators $R$ of weight zero on the algebra $U_3(F)$ of upper-triangular matrices of order three over a field of characteristic 0. For this, we apply the following three ingredients: properties of $R(1)$,…
In this paper, we construct and classify a class of non-weight modules over the BMS-Kac-Moody algebra, which are free modules of rank one when restricted to the universal enveloping algebra of the Cartan subalgebra (modulo center). We give…
With the goal of computing the Grothendieck group of certain multigraded infinite polynomial rings and the $K$-series of infinite matrix Schubert spaces, we introduce a new type of $\Gamma$-graded $k$-algebra (which we call a PDCF algebra)…
We prove that all Rota-Baxter operators on a quadratic division algebra are trivial. For nonzero weight, we state that all Rota-Baxter operators on the simple odd-dimensional Jordan algebra of bilinear form are projections on a subalgebra…
A commutative associative algebra $A$ over ${\mathbb C}$ with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for $A$ as a vertex algebra and the modules for $A$ as an…
A relative Rota-Baxter algebra is a generalization of a Rota-Baxter algebra. Relative Rota-Baxter algebras are closely related to dendriform algebras. In this paper, we introduce bimodules over a relative Rota-Baxter algebra that fits with…
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…
In this paper, we shall describe all the Rota-Baxter operators with any weight on split semi-quaternion algebra. Firstly, we give the matrix characterization of the Rota-Baxter operator on split semi-quaternion algebra. Then we give 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…
In this paper, we first construct a graded Lie algebra which characterizes Rota-Baxter operators on an anti-flexible algebra as Maurer-Cartan elements. Next, we study infinitesimal deformations of bimodules over anti-flexible algebras. We…
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…
There is a Rota-Baxter algebra structure on the field $A=\mathbf{k}((t))$ with $ P$ being the projection map $A=\mathbf{k}[[t]]\oplus t^{-1}\mathbf{k}[t^{-1}]$ onto $ \mathbf{k}[[ t]]$. We study the representation theory and…
We give a complete and rigorous classification of homogeneous weight $0$ Rota--Baxter operators on the Block-type Witt algebra $B(q)$, assuming the operator has integral degree $(k,k') \in \mathbb{Z}^2$. A key correction is established in…
We classify simple weight modules over infinite dimensional Weyl algebras and realize them using the action on certain localizations of the polynomial ring. We describe indecomposable projective and injective weight modules and deduce from…
Rota-Baxter groups with weights $\pm 1$ have attracted quite much attention since their recent introduction, thanks to their connections with Rota-Baxter Lie algebras, factorizations of Lie groups, post- and pre-Lie algebras, braces and…
We state that all Rota-Baxter operators of nonzero weight on Grassmann algebra over a field of characteristic zero are projections on a subalgebra along another one. We show the one-to-one correspondence between the solutions of associative…
In this paper, first we introduce the notion of reflections on quadratic Rota-Baxter Lie algebras of weight $\lambda$, and show that they give rise to solutions of the classical reflection equation for the corresponding triangular Lie…
The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case…
Universal enveloping Rota-Baxter algebras of preassociative and postassociative algebras are constructed. The question of Li Guo is answered: the pair of varieties (Rota-Baxter algebras of nonzero weight,postassociative algebras) is a…