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

Journal Article · Sat Feb 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4863898· OSTI ID:22251558

Pei, Jun ^[1]; Bai, Chengming ^[2]; Guo, Li ^[1]

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1. Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000 (China)
2. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071 (China)

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)⋉{sub ad{sup *}} sl (2,C){sup *}. They also give rise to three-dimensional pre-Lie algebras which in turn yield solutions of the classical Yang-Baxter equation in other six-dimensional Lie algebras.

• OSTI ID: 22251558
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EQUATIONS
MATHEMATICAL SOLUTIONS
SL GROUPS