论文标题
rota-baxter躺在双子，经典的杨巴克斯特方程和特殊的l树状伴侣
Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras
论文作者
论文摘要
我们在hanin三重方法中建立了rota巴克斯特的双重结构。明确的，Rota-baxter Lie Bialgebras的特征是将匹配的Lie代数和Lie代数的Manin Triple概括为Rota-Baxter Lie代数的背景。串联案例导致在Rota-baxter Lie代数中引入了可允许的经典杨巴克斯特方程（CYBE），为此，反对称溶液会导致rota-baxter lie bialgebras。引入了Rota-Baxter Lie代数和Rota-Baxter Pre-Lie代数的$ \ Mathcal {O} $ - 运算符的概念，以生成可允许Cybe的反对称溶液。此外，扩展了重量零代数的众所周知的属性，引起了前代代数，rota-baxter重量为零的bialgebra bialgebra a bialgebra具有独立兴趣的双质体结构，即具有特殊的l-Dendriform bialgebera，这对lie cement a live a livelent a live a live cement a evelry selliant pece in selly in exe invariant pee invariant ce n invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant invariant。这种诱导也被认为是相应的Manin三元组和匹配对之间的归纳。最后，可允许的cybe的反对称溶液零重量为零的代数为特殊的l树状型双gebras。特别是，重量为零的旋转代数和rota-baxter重量零代数均可用于构建特殊的L树突状代数。
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.
