一个新的Lie代数及其扩展Lie代数与应用

A New Lie Algebra and Its Expanding Lie Algebras as Well as Applications

构造了一类新的Lie代数,然后得到了这类Lie代数的三类扩展半单Lie代数,作为它们的应用,我们引进了两类等谱问题,利用屠格式得到了两类可积系统,并利用二次型恒等式得到了一类可积系统的Hamilton结构.

A new Lie algebra is constructed in tile paper. Then three kinds of expanding semisimple Lie algebras are introduced. As their application examples, two isospectral problems are established for which two integrable systems are obtained by employing the Tu scheme. One of them possesses Hamiltonian structure which can be produced by the use of tile quadratic-form identity.