论文标题
半胶合谎言代数中的可整合三元组
Integrable triples in semisimple Lie algebras
论文作者
论文摘要
我们将所有可集成的三元组分为简单的代数，直至等效。这个问题的重要性源于以下事实：对于每个这样的等价类别，一个人都可以构建Bi-Hamiltonian PDE的相应集成层次结构。 $ \ mathfrak {sl} _2 $中最简单的三重$（f，0，e）$对应于kdv层次结构，而triple $（f，0，e_θ）$，其中$ f $是负面简单的根矢量的总和，$e_θ$是简单的lie lie lie lie lie algebra的最高根源，是drinf by drinf drinf hy drinf b drinf b drinf b drinf。
We classify all integrable triples in simple Lie algebras, up to equivalence. The importance of this problem stems from the fact that for each such equivalence class one can construct the corresponding integrable hierarchy of bi-Hamiltonian PDE. The simplest integrable triple $(f,0,e)$ in $\mathfrak{sl}_2$ corresponds to the KdV hierarchy, and the triple $(f,0,e_θ)$, where $f$ is the sum of negative simple root vectors and $e_θ$ is the highest root vector of a simple Lie algebra, corresponds to the Drinfeld-Sokolov hierarchy.
