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Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields IV: An F4 example

Litterick, Alastair and Bannuscher, Falk and Uchiyama, Tomohiro (2022) 'Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields IV: An F4 example.' Journal of Group Theory, 25 (3). pp. 527-541. ISSN 1433-5883

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Abstract

Let k be a nonperfect 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 nonabelian k-subgroup H of G that is G-completely reducible but not G-completely reducible over k, and the first example of a connected nonabelian k-subgroup H′ 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′ only.

Item Type: Article
Uncontrolled Keywords: algebraic groups; complete reducibility; rationality; geometric invariant theory; spherical buildings; pseudo-reductive groups
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 03 Dec 2021 15:06
Last Modified: 08 Jun 2022 15:46
URI: http://repository.essex.ac.uk/id/eprint/31596

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