仿射Kac-Moody李代数三阶自同构的分类(英文)

A Classification of Order 3 Automorphismsof Affine Kac-Moody Algebras

有限维李代数的自同构理论已很完善，但仿射型Ｋａｃ－Ｍｏｏｄｙ李代数的自同构理论尚需进一步研究。首先证明了仿射Ｋａｃ－Ｍｏｏｄｙ代数自同构的一些重要性质，后对三阶自同构进行分类。同时计算了每一共轭类的不动点集。作为推论得到仿射Ｋａｃ－Ｍｏｏｄｙ代数三阶自同构共轭的充要条件是其不动点集同构。

Some properties of automorphisms of affine Kac-Moody algebras are given.Using this,we can give an explicit,complete and non-redudant set of conjugate classes of order 3 automorphisms of affine Kac-Moody algebras,also we can compute their fixed points sets.As a conclusion,we have that two automorphisms of order 3 are conjugate if and only if their fixed points sets are isomorphic.We only give the main outline here,omitting the tidious computations.