Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields I

JOURNAL OF ALGEBRA

卷:463

Article

Uchiyama, Tomohiro¹ 

[1] Univ Auckland, Dept Math, Private Bag 92019, Auckland 1142, New Zealand

关键词: Algebraic groups;    Complete reducibility;    Separability;    Spherical buildings;   

DOI  :  10.1016/j.jalgebra.2016.05.023

来源: Elsevier

【 摘 要 】

Let k be a nonperfect field of characteristic 2. Let G be a k-split simple algebraic group of type E-6 (or G(2)) defined over k. In this paper, we present the first examples of non-abelian non-G-completely reducible k-subgroups of G which are G-completely reducible over k. Our construction is based on that of subgroups of G acting non-separably on the unipotent radical of a proper parabolic subgroup of G in our previous work. We also present examples with the same property for a non-connected reductive group G. Along the way, several general results concerning complete reducibility over nonperfect fields are proved using the recently proved Tits center conjecture for spherical buildings. In particular, we show that under mild conditions a connected k-subgroup of G is pseudo reductive if it is G-completely reducible over k. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free