Gradings by Groups on Graded Cartan Type Lie Algebras

TL;DR

This paper classifies all gradings by certain abelian groups on simple graded Cartan type Lie algebras over fields with characteristic p > 2, providing a comprehensive understanding of their grading structures.

Contribution

It offers a complete classification of gradings by abelian groups without elements of order p on simple graded Cartan type Lie algebras, a previously uncharted area.

Findings

All such gradings are explicitly described.

The classification covers all simple graded Cartan type Lie algebras.

Provides a foundation for further structural analysis.

Abstract

In this paper we describe all gradings by abelian groups without elements of order p, where p > 2 is the characteristic of the base field, on the simple graded Cartan type Lie algebras.