非交换广义拉克斯对、经典Yang-Baxter方程和PostLie代数
Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
摘要：
通过引入非交换的广义拉克斯对、扩展的$\calo$-算子和扩展的经典Yang-Baxter方程的概念，推广了（广义）拉克斯对及其相关的$O$-算子和（修正的）经典Yang-Baxter方程的经典研究.在此背景下，我们研究了非交换广义$r$ -矩阵变换和相关的双李代数结构。建立了推广的$O$ -算子与推广的经典Yang-Baxter方程之间的关系，特别是对于自对偶李代数.这种关系使我们能够获得明确的描述的Manin三元组的一类新的李双代数。此外，我们表明，一个自然的结构PostLie代数是背后的$O$ -运营商，并适合在设置的三重李代数，产生自对偶nonabel广义拉克斯对。
英文摘要：
We generalize the classical study of (generalized) Lax pairs and the related $O$-operators and the (modified) classical Yang-Baxter equation by introducing the concepts of nonabelian generalized Lax pairs, extended $\calo$-operators and the extended classical Yang-Baxter equation. We study in this context the nonabelian generalized $r$-matrix ansatz and the related double Lie algebra structures. Relationship between extended $O$-operators and the extended classical Yang-Baxter equation is established, especially for self-dual Lie algebras. This relationship allows us to obtain explicit description of the Manin triples for a new class of Lie bialgebras. Furthermore, we show that a natural structure of PostLie algebra is behind $O$-operators and fits in a setup of triple Lie algebra that produces self-dual nonabelian generalized Lax pairs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
