The Restricted Ermolaev Algebra and F₄

ABSTRACT

We investigate the simple Lie algebra of type F₄ over an algebraically closed field of characteristic three. In this article, we show that the first Ermolaev algebra makes an appearance as a maximal subalgebra of F₄ and prove this using old results of Kuznetsov, Kostrikin, and Ostrik about graded depth-one simple Lie algebras over fields of characteristic three.

Keywords:

• characteristic three
• Ermolaev algebra
• nilpotent orbits

2000 AMS Subject Classification:

• 17B45

Acknowledgments

The author would like to thank Alexander Premet for his observations on Er(1; 1)⁽¹⁾ and comments on earlier drafts of the work, and David Stewart for his useful GAP advice. We also acknowledge Alex Kubiesa, who discovered a 26-dimensional maximal subalgebra of F₄ which may well be conjugate to L under the adjoint action of G.

Funding

The author acknowledges the support of an EPSRC Doctoral Training Award for this research.