Computations with reachable elements in simple Lie algebras

TL;DR

This paper presents computational results on reachable elements in simple Lie algebras of exceptional type, confirming classifications, answering open questions, and extending recent classical type results using GAP4.

Contribution

It provides computational verification of classifications and extends classical results to exceptional Lie algebras using GAP4.

Findings

Confirmed classification of reachable elements by Elashvili and Grelaud

Answered a question posed by Panyushev

Extended Yakimova's results to exceptional Lie algebras

Abstract

We report on some computations with reachable elements in simple Lie algebras of exceptional type within the SLA package of GAP4. These computations confirm the classification of such elements by Elashvili and Grelaud. Secondly they answer a question from Panyushev. Thirdly they show in what way a recent result of Yakimova for the Lie algebras of classical type extends to the exceptional types.