Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices
- Resource Type
- Authors
- Mengping Wang; Yongsheng Cheng; Linli Wu
- Source
- Advances in Mathematical Physics, Vol 2017 (2017)
- Subject
- Pure mathematics
Article Subject
Applied Mathematics
Physics
QC1-999
010102 general mathematics
Dimension (graph theory)
Zero (complex analysis)
General Physics and Astronomy
01 natural sciences
Nonlinear Sciences::Exactly Solvable and Integrable Systems
Mathematics::Quantum Algebra
0103 physical sciences
Lie algebra
010307 mathematical physics
0101 mathematics
Algebra over a field
Mathematics
- Language
- English
- ISSN
- 1687-9120
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 zero) on the 3-dimensional Lie algebras g. Furthermore, we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ⋉ad⁎ g⁎ and the induced left-symmetry algebra structures on g.