G_2型单代数群的单限制模的G_1-扩张

G_1-extension for the simple module of simple algebraic group of type G_2

摘要: 设 G是特征 p的代数闭域 K上单连通半单代数群 ,G1 是第一次 Frobenius态射的核 ,即 G1 =Ker F.要确定单 G模的 G-扩张必须先确定限制单模的 G1 -扩张 .本文就是确定出特征 p=5的代数闭域 K上G2 型单代数群的所有单 G1 -模的扩张群

Abstract: Let G be the simply connected semisimple algebraic group over algebraically closed field K in characteristic p,and G 1 be the kernel of the first Frobenius morphism of G,i.e G 1=KerF.All G 1 Extensions for the simple module of simple algebraic group type G 2 over algebraic closed field K in characteric five are determined in this note.