Irreducible L-modules of Modular Lie algebras

TL;DR

This paper investigates the classification of all irreducible modules of modular Lie algebras, emphasizing the role of the p-mapping and induced modules in the decomposition process.

Contribution

It introduces a method to decompose modular Lie algebras into irreducible modules using properties of induced modules and explores this through specific examples.

Findings

Decomposition of modular Lie algebras into irreducible modules achieved

Establishment of a correspondence between induced modules and original modules

Demonstrations via examples of the decomposition process

Abstract

The main objective of this project is to determine all irreducible modules of a given modular Lie algebra. In contrast to ordinary Lie algebras, modular Lie algebras require an additional structure known as the p-mapping. The minimal p-envelope of a modular Lie algebra is restrictable, and there exists a one-to-one correspondence between the induced modules and certain original modules. By exploiting the properties of induced modules, this project aims to decompose a modular Lie algebra L into irreducible L- modules. Several examples will be presented to demonstrate how such decompositions can be achieved for specific modular Lie algebras.