Complete reducibility of subgroups of reductive algebraic groups over non-perfect fields IV: An 𝐹4 example

Author:

Bannuscher Falk1,Litterick Alastair2,Uchiyama Tomohiro3

Affiliation:

1. Fakultät für Mathematik , Ruhr-Universität Bochum , Bochum , Germany

2. Department of Mathematical Sciences , University of Essex , Colchester , United Kingdom

3. Faculty of International Liberal Arts , Soka University , Hachioji , Japan

Abstract

Abstract Let 𝑘 be a non-perfect separably closed field. Let 𝐺 be a connected reductive algebraic group defined over 𝑘. We study rationality problems for Serre’s notion of complete reducibility of subgroups of 𝐺. In particular, we present the first example of a connected non-abelian 𝑘-subgroup 𝐻 of 𝐺 that is 𝐺-completely reducible but not 𝐺-completely reducible over 𝑘, and the first example of a connected non-abelian 𝑘-subgroup H H^{\prime} of 𝐺 that is 𝐺-completely reducible over 𝑘 but not 𝐺-completely reducible. This is new: all previously known such examples are for finite (or non-connected) 𝐻 and H H^{\prime} only.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Complete reducibility for Lie subalgebras and semisimplification;European Journal of Mathematics;2023-12

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