The stabilizer group of adjoint-invariant forms

TL;DR

This paper defines the stabilizer group of adjoint-invariant forms on complex simple Lie algebras, extending previous results and contributing to the understanding of symmetry groups in Lie algebra theory.

Contribution

It introduces a new definition of the stabilizer group for adjoint-invariant forms, extending prior work by Kable.

Findings

Defined the stabilizer group for adjoint-invariant forms.

Extended Kable's previous results on Lie algebra symmetries.

Provided a framework for analyzing invariance in complex simple Lie algebras.

Abstract

In this note we define the stabilizer group of any adjoint-invariant $l$-form on a complex simple Lie algebra. This result partially extend a previous result by Kable.