推广的一类Lie代数及其相关的一族可积系统

对已知的Lie代数An-1作直接推广得到一类新的Lie代数gl(n,C).为应用方便，本文只考虑Lie代数gl(3,C)情形.构造了gl(3,C)的一个子代数，通过对阶数的规定，得到了一类新的loop代数.作为其应用，设计了一个新的等谱问题，得到了一个新的Lax对.利用屠格式获得了一族新的可积系统，具有双Hamilton结构,且是Liouville可积系.作为该方程族的约化情形，得到了新的耦合广义Schrdinger方程.关键词：Lie代数可积系Hamilton结构

An extension of Lie algebra and a related integrable system

A direct extension of the known Lie algebra An-1 is presented, a new Lie algebra gl(n,C) is obtained. For the sake of application convenience, Lie algebra gl(3,C) is only considered, whose subalgebra is constructed. By the definition of the subalgebra gradation,a new loop algebra is shown. As its application, an isospectral problem is designed. It follows that a new Lax pair is obtained. By making use of Tu scheme, a family of new Liouville integrable system is resented, which possesses a bi Hamiltonian structure. As the reduction case of the hierarchy obtained, a new coupled generalized Schrdinger equation is obtained.