Non-separability and complete reducibility: En examples with an application to a question of Kulshammer

被引：4

作者：

Uchiyama, Tomohiro ^{[1
]}

机构：

[1] Natl Taiwan Univ, Natl Ctr Theoret Sci, Math Div, 1,Sect 4,Roosevelt Rd, Taipei, Taiwan

来源：

JOURNAL OF GROUP THEORY | 2017年 / 20卷 / 05期

关键词：

ALGEBRAIC-GROUPS; IRREDUCIBLE SUBGROUPS; CONJUGACY CLASSES; REDUCTIVE GROUPS; LIE-ALGEBRAS; REPRESENTATIONS; SEPARABILITY; ORBITS;

D O I：

10.1515/jgth-2017-0005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a simple algebraic group of type E-n (n = 6; 7; 8) defined over an algebraically closed field k of characteristic 2. We present examples of triples of closed reductive groups H < M < G such that H is G-completely reducible, but not M-completely reducible. As an application, we consider a question of Kulshammer on representations of finite groups in reductive groups. We also consider a rationality problem for G-complete reducibility and a problem concerning conjugacy classes.

引用

页码：925 / 944

页数：20