Reductions of Integrable Equations and Automorphic Lie Algebras
Reductions of Integrable Equations and Automorphic Lie Algebras
复制标题
可积方程和自守李代数的约简
DOI：
10.1142/9789812702142_0022
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
A. Mikhailov
中科院分区：
文献类型：
--
作者：
S. Lombardo;A. Mikhailov
我们定义了一类对谱参数X有合理依赖的广义Lax算子族，并讨论了约简问题。我们发展了约简群方法，并研究了相关的无限维李代数。这自然引出了自同构李代数的概念。自同构李代数最初是在可积系统的背景下出现的，但人们相信它们本身就具有数学意义。
We define a rather general family of Lax operators with rational dependence on the spectral parameter X and discuss the problem of reductions. We develop the reduction group approach and study the associated infinite dimensional Lie algebras. This naturally leads to the concept of automorphic Lie algebras. Automorphic Lie algebras arise originally in the context of integrable systems but it is to believe that they are of mathematical interest on their own right.