Involutions of type $G_2$ over a field of characteristic 2

TL;DR

This paper classifies involutions on automorphism groups of octonion algebras over fields of characteristic 2, detailing their fixed point groups and providing a comprehensive understanding of their structure.

Contribution

It offers the first classification of involutions of type G_2 over fields of characteristic 2 and describes their fixed point subgroups, advancing the theory of algebraic groups in characteristic 2.

Findings

Classification of involutions on automorphism groups of octonion algebras

Description of fixed point groups of these involutions

New insights into algebraic groups in characteristic 2

Abstract

In this paper we give a classification of classes of involutions on an automorphism group of an octonion algebra over fields of characteristic 2, and describe the classes of their fixed point groups.