## 12 Citations

### Representations and modules of Rota–Baxter algebras

- MathematicsAsian Journal of Mathematics
- 2021

We give a broad study of representation and module theory of Rota-Baxter algebras. Regular-singular decompositions of Rota-Baxter algebras and Rota-Baxter modules are obtained under the condition of…

### Rota-Baxter $C^{\ast}$-algebras

- Mathematics
- 2021

This paper introduces the notion of Rota-Baxter C∗-algebras. Here a RotaBaxter C∗-algebra is a C∗-algebra with a Rota-Baxter operator. Symmetric Rota-Baxter operators, as special cases of Rota-Baxter…

### Modules of polynomial Rota-Baxter Algebras and matrix equations

- Mathematics
- 2020

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}…

### Rota-Baxter Modules Toward Derived Functors

- Mathematics
- 2017

In this paper we study Rota-Baxter modules with emphasis on the role played by the Rota-Baxter operators and the resulting difference between Rota-Baxter modules and the usual modules over an…

### Rota-Baxter Modules Toward Derived Functors

- MathematicsAlgebras and Representation Theory
- 2018

In this paper we study Rota-Baxter modules with emphasis on the role played by the Rota-Baxter operators and the resulting difference between Rota-Baxter modules and the usual modules over an…

### Monomial Rota-Baxter operators of nonzero weight on $F[x,y]$ coming from averaging operators

- Mathematics
- 2022

The intensive study of Rota—Baxter operators on the polynomial algebra F [ x ] has been started with the work of S.H. Zheng, L. Guo, and M. Rosenkranz (2015). We deal with the case of two variables…

### Representations and cohomologies of relative Rota-Baxter Lie algebras and applications

- MathematicsJournal of Algebra
- 2022

### Factorizable Lie Bialgebras, Quadratic Rota–Baxter Lie Algebras and Rota–Baxter Lie Bialgebras

- MathematicsCommunications in Mathematical Physics
- 2022

In this paper, first we introduce the notion of quadratic Rota–Baxter Lie algebras of arbitrary weight, and show that there is a one-to-one correspondence between factorizable Lie bialgebras and…

### Injective Rota–Baxter Operators of Weight Zero on F[x]

- MathematicsMediterranean Journal of Mathematics
- 2021

Rota–Baxter operators present a natural generalization of integration by parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz conjectured that every injective Rota–Baxter…

## References

SHOWING 1-10 OF 18 REFERENCES

### Representations of Rota-Baxter algebras and regular singular decompositions

- Mathematics
- 2016

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 Spaces of the Jordan Plane

- Mathematics
- 2012

We investigate relations between the properties of an algebra and its varieties of finite-dimensional module structures, on the example of the Jordan plane R = k ⟨ x, y ⟩ /(xy − yx − y 2). A complete…

### A Parametric Family of Subalgebras of the Weyl Algebra II. Irreducible Modules

- Mathematics
- 2012

An Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra A_h generated by elements x,y, which satisfy…

### A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMS

- Mathematics
- 2012

An Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra Ah generated by elements x, y, which satisfy…

### Examples in non-commutative projective geometry

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1994

Let A = k ⊕ ⊕n ≥ 1An connected graded, Noetherian algebra over a fixed, central field k (formal definitions will be given in Section 1 but, for the most part, are standard). If A were commutative,…

### Noncommutative graded domains with quadratic growth

- Mathematics
- 1995

Letk be an algebraically closed field, and letR be a finitely generated, connected gradedk-algebra, which is a domain of Gelfand-Kirillov dimension two. Write the graded quotient ringQ(R) ofR…

### Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

- Mathematics
- 2000

Abstract:This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure…

### Jordanian plane

- Mathematics
- 2008

In this article, we consider the Jordanian plane over a field of arbitrary characteristic. We describe the prime spectrum, the group of automorphisms, and derivations of the Jordanian plane. We study…