Maximal abelian subgroups of Spin groups and some exceptional simple Lie groups

TL;DR

This paper classifies specific abelian subgroups within exceptional Lie groups and Spin groups, focusing on those with particular centralizer properties, advancing understanding of their subgroup structures.

Contribution

It provides a classification of closed and finite abelian subgroups with specified centralizer dimensions in exceptional Lie groups and Spin groups.

Findings

Classified closed abelian subgroups of G2, F4, and Aut(so(8)) with maximal centralizers.

Identified finite abelian subgroups of certain Spin and half-Spin groups with finite centralizers.

Enhanced understanding of subgroup structures in exceptional Lie and Spin groups.

Abstract

We classify closed abelian subgroups of the simple groups $G_2$, $F_4$, $Aut(so(8))$ having centralizer the same dimension as the dimension of the subgroup, as well as finite abelian subgroups of certain spin and half-spin groups having finite centralizer.