Maximal abelian subgroups of compact simple Lie groups of type E

TL;DR

This paper classifies certain abelian subgroups within compact simple Lie groups of type E, focusing on those with centralizers of equal dimension and detailing their Weyl groups.

Contribution

It provides a comprehensive classification of maximal abelian subgroups with specific centralizer properties in compact simple Lie groups of type E.

Findings

Classification of closed abelian subgroups with equal centralizer and subgroup dimensions.

Description of Weyl groups associated with these maximal abelian subgroups.

Insights into the structure of abelian subgroups in exceptional Lie groups.

Abstract

We classify closed abelian subgroups of a compact simple Lie group of adjoint type and of type E having centralizer of the same dimension as the dimension of the subgroup and describe Weyl groups of maximal abelian subgroups.