Shuhan图分类及其应用

Classification and its application of Shuhan diagram

Shuhan图是一个图论、Kac-Moody代数和矩阵论等学科的交叉研究对象.首先给出了Shuhan图的定义,再利用图论的分类方法得到了所有连通的Shuhan图:A_(n)^((a))(n≥2)、D_(n)^((a))(n≥4)、E_(6)^((a))、E_(7)^((a))、E_(8)^((a)),这证明了连通的非扭单边仿射Lie代数对应的Dynkin图恰好是全部的最小点数为1的连通Shuhan图.进一步地,由Shuhan图的性质可知,任意Shuhan图都是由若干连通Shuhan图并在一起的,这就给出了Shuhan图的完整分类.

Shuhan diagram is an interdisciplinary research object of graph theory,Kac-Moody algebra and matrix theory.Firstly,Shuhan diagram is defined,and then using the classification method of graph theory,all connected Shuhan diagrams:A_(n)^((a))(n≥2)、D_(n)^((a))(n≥4)、E_(6)^((a))、E_(7)^((a))、E_(8)^((a)) are obtained,this proves that Dynkin diagram corresponding to the connected non-twisted single-side affine Lie algebra is exactly all connected Shuhan diagram with the minimum number of 1.Furthermore,according to the properties of Shuhan diagrams,any Shuhan diagram is composed of several connected Shuhan diagrams,which gives a complete classification of Shuhan diagrams.