# Rota-Baxter operators on sl (2,C) and solutions of the classical Yang-Baxter equation

@article{Pei2013RotaBaxterOO, title={Rota-Baxter operators on sl (2,C) and solutions of the classical Yang-Baxter equation}, author={Jun Pei and Chengming Bai and Li Guo}, journal={Journal of Mathematical Physics}, year={2013}, volume={55}, pages={021701} }

We explicitly determine all Rota-Baxter operators (of weight zero) on sl (2,C) under the Cartan-Weyl basis. For the skew-symmetric operators, we give the corresponding skew-symmetric solutions of the classical Yang-Baxter equation in sl (2,C), confirming the related study by Semenov-Tian-Shansky. In general, these Rota-Baxter operators give a family of solutions of the classical Yang-Baxter equation in the six-dimensional Lie algebra sl (2,C)⋉ ad * sl (2,C)*. They also give rise to three…

## 26 Citations

### Rota–Baxter Operators of Nonzero Weight on a Complete Linear Lie Algebra of Order Two

- MathematicsAlgebra and Logic
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Rota–Baxter operators for associative algebras appeared in Baxter’s paper [1] as part of the study of integral operators emerging in probability theory and mathematical statistics. Independently, in…

### Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical -Matrices

- Mathematics
- 2017

Our aim is to classify the Rota-Baxter operators of weight 0 on the 3-dimensional Lie algebra whose derived algebra’s dimension is 2. We explicitly determine all Rota-Baxter operators (of weight…

### Rota–Baxter Operators on Quadratic Algebras

- MathematicsMediterranean Journal of Mathematics
- 2018

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…

### Classification of Rota-Baxter operators on semigroup algebras of order two and three

- MathematicsCommunications in algebra
- 2019

All the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra are determined by directly solving the defining equations of the operators.

### Rota–Baxter Operators on Pre-Lie Superalgebras

- Mathematics
- 2019

In this paper, we study Rota–Baxter operators and super $$\mathcal {O}$$O-operator of associative superalgebras, Lie superalgebras, pre-Lie superalgebras and L-dendriform superalgebras. Then we give…

### Construction of free Lie Rota-Baxter superalgebra via Gr\"{o}bner-Shirshov bases theory

- Mathematics
- 2021

In this paper, we construct free Lie Rota-Baxter superalgebra by using Gröbner-Shirshov bases theory. We firstly construct free operated Lie superalgebras by the operated super-Lyndon-Shirshov…

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- Mathematics
- 2017

We generalize the Lyndon–Shirshov words to the Lyndon–Shirshov Ω-words on a set X and prove that the set of all the nonassociative Lyndon–Shirshov Ω-words forms a linear basis of the free Lie…

### The structure of monomial Rota-Baxter operators on k[x]

- Mathematics
- 2015

Rota-Baxter operators were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. The polynomial algebra…

### Classification of monomial Rota-Baxter operators on k[x]

- Mathematics
- 2015

Rota-Baxter operators were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. The polynomial algebra…

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