Group gradings on simple Lie algebras of type A in positive characteristic

TL;DR

This paper studies how finite abelian groups can be used to grade simple Lie algebras of type A over algebraically closed fields with positive characteristic, expanding understanding of their structural symmetries.

Contribution

It classifies gradings by finite abelian groups on simple Lie algebras of type A in positive characteristic, a case less explored in existing literature.

Findings

Classification of gradings by finite abelian groups on  over algebraically closed fields

Results applicable for characteristics not dividing n or equal to 2

Provides a framework for understanding symmetries in Lie algebra structures

Abstract

In this paper we consider gradings by a finite abelian group $G$ on the Lie algebra $\mathfrak{sl}_n(F)$ over an algebraically closed field $F$ of characteristic different from 2 and not dividing $n$.