The Restricted Ermolaev algebra and $F_4$

TL;DR

This paper explores the structure of the simple Lie algebra of type F4 over a field of characteristic 3, revealing that the restricted Ermolaev algebra appears as a maximal subalgebra, thus contributing to the understanding of algebraic structures in positive characteristic.

Contribution

It demonstrates that the restricted Ermolaev algebra is a maximal subalgebra of F4 in characteristic 3, providing new insights into the subalgebra structure of Lie algebras in positive characteristic.

Findings

Restricted Ermolaev algebra is a maximal subalgebra of F4 in characteristic 3

Identification of subalgebra structures in Lie algebra F4 over fields of characteristic 3

Advances understanding of algebraic structures in positive characteristic fields

Abstract

We investigate the simple Lie algebra of type $F_4$ over an algebraically closed field of characteristic $p=3$. In this article we show that the restricted Ermolaev algebra makes an appearance as a maximal subalgebra of $F_4$.