仿射型李代数g(A)的某些自同构群

§0 引言 A=(α_(ij))是n阶广义Cantan矩阵,即A满足:ⅰ)α_(ii)=2,i=1,…n。ⅱ)当i≠j时,α_(ij)是非正整数。ⅲ) a_(ij)=0 α_(ji)=0。 h是复数域C上2n-l维向量空间,h是h的对偶空间。Π={α_1,…α_n},Π分别是h与h中线性无关子集,满足     

RESEARCH ANNOUNCEMENTS On Certain Automorphism Groups of an Affine Lie Algebra

Let A be an n×n symmetrizable generalized Cartan matrix,g(A)the Kac-Moody Lie algebra associated with A,h the Cartan subalgebra of g(A).Π and Π_vare the root basis and the dual root basis of g(A)respectively.Δ and W are theroot system and the Weyl group of g(A)respectively. Then g(A)=h+∑g_n is a