Symmetries of abelian ideals of Borel subalgebras

TL;DR

This paper characterizes the automorphism group of the poset of abelian ideals within Borel subalgebras of complex simple Lie algebras, extending previous work by Suter.

Contribution

It provides a detailed description of the automorphism group, offering new insights into the symmetries of abelian ideals in Lie algebra theory.

Findings

Complete characterization of the automorphism group.

Extension of Suter's previous results.

Deeper understanding of symmetries in Lie algebra structures.

Abstract

Elaborating on a paper by Suter, we provide a detailed description of the automorphism group of the poset of abelian ideals in a Borel subalgebra of a finite dimensional complex simple Lie algebra.