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… 

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