Maximal abelian subgroups of compact matrix groups

TL;DR

This paper classifies certain abelian subgroups within automorphism groups of compact classical Lie algebras, focusing on those with centralizers of equal dimension and analyzing their Weyl groups.

Contribution

It provides a classification of maximal abelian subgroups with specific centralizer properties and describes their Weyl groups in compact classical Lie algebras.

Findings

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

Description of Weyl groups associated with maximal abelian subgroups.

Insights into the structure of automorphism groups of compact classical Lie algebras.

Abstract

We classify closed abelian subgroups of the automorphism group of any compact classical simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup, and describe Weyl groups of maximal abelian subgroups.