实半單李代数的約化根系及约化Weyl羣

DETERMINATION OF THE RESTRICTED ROOT SYSTEMS AND RESTRICTED WEYL GROUPS OF ALL REAL SEMISIMPLE LIE ALGEBRAS

1.关于实半单李代数的約化Weyl羣,陈仲沪曾从实半单李代数的一个具有极大环面部分的Cartan子代数出发进行过討論,并且算出典型复李代数的实型的約化Weyl羣。就約化Weyl羣这一概念本身来看,从具有极大向量部分的Cartan子代数出发来討論和計算,似乎更直接一些。1960年Satake首先給出了典型实李代数的Satake图。

Starting from Cartan sub-algebras with maximum torus parts, C. H. Cheng has determined the restricted weyl groups of the real forms of classical complex Lie algebras. S. Arakl, starting from Caftan sub-algebras with maximum vector parts, has studied the restricted root systems of real semi-simple Lie algebras and given the Satake diagrams of all real semisimple Lie algebras. On the basis of S. Araki the author determines in the present paper the restricted root systems and restricted weyl groups of all real semi-simple Lie algebras.