论文标题
古典lie-yamaguti Yang-baxter方程和lie-yamaguti bialgebras
The classical Lie-Yamaguti Yang-Baxter equation and Lie-Yamaguti bialgebras
论文作者
论文摘要
在本文中，我们开发了lie-yamaguti代数的双重理论。为此，我们利用了两种类型的兼容条件：本地生殖器条件和双重结构。我们在Lie-Yamaguti代数中定义了经典的Yang-Baxter方程，并表明对经典Yang-Baxter方程的解决方案对应于相对Rota-Baxter Operator相对于Coadexhight表示。此外，我们将BAI在[1]和[19]中的Semonov-Tian-Shansky中概括为Lie-Yamaguti代数的背景。然后，我们介绍了匹配的一对lie-yamaguti代数的概念，这使我们在使用bialgebras的Manin Triple方法之后，将双重结构lie-yamaguti bialgebras提出。我们证明了匹配的成对，lie-yamaguti代数的曼宁三元组以及双重结构lie-yamaguti bialgebras等效。最后，我们澄清说，局部的合生疾病是lie-yamaguti bialgebras的双重结构的特殊情况。
In this paper, we develop the bialgebra theory for Lie-Yamaguti algebras. For this purpose, we exploit two types of compatibility conditions: local cocycle condition and double construction. We define the classical Yang-Baxter equation in Lie-Yamaguti algebras and show that a solution to the classical Yang-Baxter equation corresponds to a relative Rota-Baxter operator with respect to the coadjoint representation. Furthermore, we generalize some results by Bai in [1] and Semonov-Tian-Shansky in [19] to the context of Lie-Yamaguti algebras. Then we introduce the notion of matched pairs of Lie-Yamaguti algebras, which leads us to the concept of double construction Lie-Yamaguti bialgebras following the Manin triple approach to Lie bialgebras. We prove that matched pairs, Manin triples of Lie-Yamaguti algebras, and double construction Lie-Yamaguti bialgebras are equivalent. Finally, we clarify that a local cocycle condition is a special case of a double construction for Lie-Yamaguti bialgebras.
