136
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

The Restricted Ermolaev Algebra and F4

ORCID Icon
 

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.

2000 AMS Subject Classification:

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.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.