A note on the rank of a restricted Lie algebra

TL;DR

This paper investigates the rank of restricted Lie algebras, explores its implications for irreducible modules, and computes the rank of the restricted contact algebra K(n), providing new insights into their structural properties.

Contribution

It introduces new results on the rank of restricted Lie algebras and calculates the rank of the restricted contact algebra K(n), advancing understanding of their module theory.

Findings

Derived bounds on the rank of restricted Lie algebras

Connected rank to dimensions of irreducible modules

Computed the rank of the restricted contact algebra K(n)

Abstract

In this short note, we study the rank of a restricted Lie algebra $(\mathfrak{g},[p])$ and give some applications, which concerns the dimensions of non-trivial irreducible modules. We also compute the rank of the restricted contact algebra $K(n)$.