تقرير
Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras
| العنوان: | Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras |
|---|---|
| المؤلفون: | Bai, Chengming, Guo, Li, Liu, Guilai, Ma, Tianshui |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Mathematics - Quantum Algebra, Mathematical Physics, 17B38, 17B62, 17B10, 16T25, 17A30, 17A36, 17D25 |
| الوصف: | We establish a bialgebra structure on Rota-Baxter Lie algebras following the Manin triple approach to Lie bialgebras. Explicitly, Rota-Baxter Lie bialgebras are characterized by generalizing matched pairs of Lie algebras and Manin triples of Lie algebras to the context of Rota-Baxter Lie algebras. The coboundary case leads to the introduction of the admissible classical Yang-Baxter equation (CYBE) in Rota-Baxter Lie algebras, for which the antisymmetric solutions give rise to Rota-Baxter Lie bialgebras. The notions of $\mathcal{O}$-operators on Rota-Baxter Lie algebras and Rota-Baxter pre-Lie algebras are introduced to produce antisymmetric solutions of the admissible CYBE. Furthermore, extending the well-known property that a Rota-Baxter Lie algebra of weight zero induces a pre-Lie algebra, the Rota-Baxter Lie bialgebra of weight zero induces a bialgebra structure of independent interest, namely the special L-dendriform bialgebra, which is equivalent to a Lie group with a left-invariant flat pseudo-metric in geometry. This induction is also characterized as the inductions between the corresponding Manin triples and matched pairs. Finally, antisymmetric solutions of the admissible CYBE in a Rota-Baxter Lie algebra of weight zero give special L-dendriform bialgebras. In particular, both Rota-Baxter algebras of weight zero and Rota-Baxter pre-Lie algebras of weight zero can be used to construct special L-dendriform algebras. Comment: 29 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2207.08703 |
| رقم الأكسشن: | edsarx.2207.08703 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |