关于特殊的实单Lie代数D_4的内共轭分类

On the Classification of Real Simple Lie Algebras D_4 by the Inner Conjugation

在[2]中,我们讨论了实单Lie代数的内共轭分类问题,但对于稍为困难的特殊实单Lie代数D作为例外,没有讨论.在[3]中,我们提到了可以利用定理2[3]直接证明内共轭的分类定理,但因为篇幅关系,没有给予详细的证明.在本文中,我们将讨论D_4的内共轭分类问题,并详细证明关于Satake图解的内共轭分类定理. 设of是实单Lie代数,g^c是f的复化,Autg^c,Intg^c,分别是g^c的自同构群和内自同构群;Aut(g),Int(g)Int(g)分别是g^c的自同构群拟内自同构群和内自同构群,其他符号参看[1].

In this paper, we consider the real forms of the complex simple Lie algebra D1. We proved that if two real forms are isomorphism then they are inner conjugated, but in the case of type DI6(i0 = l ,3,4)there exist three forms and in the-case of type DⅢ6(i0 = 3,4) there exist two forms which are isomorphism but are not inner conjugated. Hence we proved the following result.Let Int(g)and Int(g)are the quasi-inner automorphism group and inner automorphism group of the real simple Lie algebra g respectively, let n be the number of real form which are associated the isomorphic Yen-Murakami graphs or the isomorphic Satake graphs, then n is equal to the number of elements of the set Int (g)/Int(g).