English
Related papers

Related papers: Representations of Polynomial Rota-Baxter Algebras

200 papers

Let k be a field of characteristic zero. We consider graded subalgebras A of k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear forms. Representations of matroids over k provide a natural description of the…

Combinatorics · Mathematics 2007-05-23 David G. Wagner

In this paper, we introduce the cohomology theory of relative Rota-Baxter operators on Leibniz algebras. We use the cohomological approach to study linear and formal deformations of relative Rota-Baxter operators. In particular, the notion…

Rings and Algebras · Mathematics 2021-02-26 Rong Tang , Yunhe Sheng , Yanqiu Zhou

In this paper, first we introduce the notion of a quadratic Lie-Yamaguti algebra and show that the invariant bilinear form in a quadratic Lie-Yamaguti algebra induces an isomorphism between the adjoint representation and the coadjoint…

Rings and Algebras · Mathematics 2022-10-24 Yunhe Sheng , Jia Zhao

The aim of this paper is first to introduce and study Rota-Baxter cosystems and bisystems as generalization of Rota-Baxter coalgebras and bialgebras, respectively, with various examples. The second purpose is to provide an alternative…

Rings and Algebras · Mathematics 2017-10-17 Tianshui Ma , Abdenacer Makhlouf , Sergei Silvestrov

A Rota-Baxter algebra $A_R$ is an algebra $A$ equipped with a distinguished Rota-Baxter operator $R$ on it. Rota-Baxter algebras are closely related to dendriform algebras introduced by Loday. In this paper, we first consider the…

Rings and Algebras · Mathematics 2022-06-22 Apurba Das , Nishant Rathee

Universal enveloping commutative Rota-Baxter algebras of pre- and postcommutative algebras are constructed. We prove that the pair of varieties (commutative Rota-Baxter algebras of nonzero weight,postcommutative algebras) is a PBW-pair and…

Rings and Algebras · Mathematics 2018-01-23 Vsevolod Gubarev

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…

Mathematical Physics · Physics 2025-12-19 Li Guo , Yan Jiang , Yunhe Sheng , You Wang

The purpose of this paper is to determine all Rota-Baxter operators on dual quaternion algebra $\mathcal{H}_d$ over the reals.

Commutative Algebra · Mathematics 2026-04-30 Hassan Oubba , Azhar Farooq , Kamran Shakoor

Let T and C be two Hilbert space operators. We prove that if T is near, in a certain sense, to an operator completely polynomially dominated with a finite bound by C, then T is similar to an operator which is completely polynomially…

Functional Analysis · Mathematics 2007-05-23 C. Badea

We define the concept of weak pseudotwistor for an algebra $(A, \mu)$ in a monoidal category $\mathcal{C}$, as a morphism $T:A\otimes A\rightarrow A\otimes A$ in $\mathcal{C}$, satisfying some axioms ensuring that $(A, \mu \circ T)$ is also…

Quantum Algebra · Mathematics 2016-04-20 Florin Panaite , Freddy Van Oystaeyen

We study a vertex operator algebra containing a tensor product of Ising models. It is a direct sum of code vertex operator algebra and its irreducible modules. Therefore, we classify all irreducible modules of code vertex operator algebras…

High Energy Physics - Theory · Physics 2007-05-23 Masahiko Miyamoto

We show that the class of Metropolis-Rota implication algebras can be given a universal axiomatization using an operation closely related to composition in oriented matroids. Lastly we describe the role of our new operation in the collapse…

Combinatorics · Mathematics 2009-02-03 Colin Bailey , Joseph Oliveira

The purpose of this paper is to study some results of constructions on Hom-Poisson superal-gebras we use the representations and Rota-Baxter operators. We introduce the structures ofn-ary Hom-Nambu Poisson superalgebras and their…

Rings and Algebras · Mathematics 2021-12-28 Othmen Ncib

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…

Rings and Algebras · Mathematics 2020-07-14 Apurba Das

Consider an algebraic equation $P(x,y)=0$ where $P\in \mathbb C[x,y] $ (or $\mathbb F[x,y]$ with $\mathbb F\subset \mathbb C$ a subfield) is a bivariate polynomial, it defines a plane algebraic curve. We provide an efficient method for…

Mathematical Physics · Physics 2024-06-03 Bertrand Eynard

We completely characterize orbit reflexivity and R-orbit reflexivity for square matrices over the real numbers. Unlike the complex case in which every matrix is orbit reflexive and C-orbit reflexivity is characterized solely in terms of the…

Functional Analysis · Mathematics 2011-12-09 Don Hadwin , Ileana Ionascu , Hassan Yousefi

Integral categories were recently developed as a counterpart to differential categories. In particular, integral categories come equipped with an integration operator, known as an integral transformation, whose axioms generalize the basic…

Category Theory · Mathematics 2019-07-26 G. S. H. Cruttwell , J. -S. P. Lemay , R. B. B. Lucyshyn-Wright

This paper presents some algorithmic techniques to compute explicitly the noetherian operators associated to a class of ideals and modules over a polynomial ring. The procedures we include in this work can be easily encoded in computer…

Commutative Algebra · Mathematics 2010-03-30 A. Damiano , I. Sabadini , D. C. Struppa

The aim of this paper is twofold. In the first part, we consider twisted Rota-Baxter operators on associative algebras that were introduced by Uchino as a noncommutative analogue of twisted Poisson structures. We construct an…

Rings and Algebras · Mathematics 2020-10-06 Apurba Das

Rota-Baxter systems are modified by the inclusion of a curvature term. It is shown that, subject to specific properties of the curvature form, curved Rota-Baxter systems $(A,R,S,\omega)$ induce associative and (left) pre-Lie products on the…

Rings and Algebras · Mathematics 2016-04-13 Tomasz Brzeziński