Isomorphy classes of k-involutions of G_2

TL;DR

This paper investigates the classification of k-involutions in algebraic groups of exceptional type G_2, extending previous work on classical groups to understand their symmetric space structures.

Contribution

It introduces the study of isomorphy classes of k-involutions for the exceptional algebraic group G_2, expanding the scope beyond classical groups.

Findings

Classified k-involutions for G_2

Established correspondence with symmetric spaces for G_2

Extended existing theories to exceptional algebraic groups

Abstract

Isomorphy classes of k-involutions have been studied for their correspondence with generalized symmetric spaces of algebraic groups. This is a continuation of papers written by A.G. Helminck and collaborators that are regarding algebraic groups of classical type. Here we begin doing the same for algebraic groups of exceptional type.