Decomposition of compact exceptional Lie groups into their maximal tori

TL;DR

This paper investigates how certain involutive automorphisms of exceptional Lie groups decompose these groups into their maximal tori by analyzing fixed point subgroups and their intersections.

Contribution

It identifies specific involutive automorphisms whose fixed point subgroup intersections yield the maximal tori of exceptional Lie groups.

Findings

Connected components of fixed point subgroup intersections match maximal tori

Explicit involutive automorphisms for groups F_4, E_6, E_7 identified

Provides a method to decompose exceptional Lie groups into maximal tori

Abstract

In this paper we treat the intersection of fixed point subgroups by the involutive automorphisms of exceptional Lie group $G= F_4, E_6, E_7$. We shall find involutive automorphisms of $G$ such that the connected component of the intersection of those fixed point subgroups coincides with the maximal torus of $G$.