Manin三元组对李可归复形代数的分类
Classification des triples de Manin pour les algèbres de Lie réductives complexes
摘要：
研究了复约化李代数$\g$的实Manin三元组和复Manin三元组.第一部分包括，并扩展到复杂的Manin三倍，我们的早期工作[德]。首先，我们推广了E. Karolinsky，关于拉格朗日子代数的分类（参见。[K1]，[K3]）。然后证明了，如果$\g$是非交换的，则$\g$的严格较小的约化复李子代数可以在$\g$的每个Manin三元组上附加另一个Manin三元组.这为归纳提供了一个强有力的工具。然后，我们分类复杂的Manin三元组，我们称之为广义Belavin-Drinfeld数据。特别地，这通过其他方法推广了A. Belavin和G. Drinfeld的某些$R$ -矩阵，即修改的三角方程的常数的解决方案（参见[BD]，定理6.1）。我们也得到了真正的Manin三元组的结果。在传递过程中，检索到A的结果。Panov [P1]对实单李代数上的某些李双代数结构进行了分类。
英文摘要：
We study real and complex Manin triples for a complex reductive Lie algebra, $\g$. The first part includes, and extends to complex Manin triples, our earlier work [De]. First, we generalize results of E. Karolinsky, on the classification of Lagrangian subalgebras (cf.[K1], [K3]). Then we show that, if $\g$ is non commutative, one can attach, to each Manin triple in $\g$, another one for a strictly smaller reductive complex Lie subalgebra of $\g$. This gives a powerful tool for induction. Then we classify complex Manin triples, in terms of what we call generalized Belavin-Drinfeld data. In particular this generalizes, by other methods, the classification of A. Belavin and G. Drinfeld of certain $R$-matrices, i.e. the solutions of modified triangle equations for constants (cf [BD], Theorem 6.1). We get also results for real Manin triples. In passing, one retrieves a result of A. Panov [P1] which classifies certain Lie bialgebras structures on a real simple Lie algebra.
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。
