Deformations of current Lie algebras. I. Small algebras in characteristic 2

Abstract

We compute low-degree cohomology of current Lie algebras extended over the 3-dimensional simple algebra, compute deformations of related semisimple Lie algebras, and apply these results to classification of simple Lie algebras of absolute toral rank 2 and having a Cartan subalgebra of toral rank one. Everything is in characteristic 2.

v3: minor changes

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• Computing subalgebras and ${\mathbb{Z}}_2$-gradings of simple Lie algebras over finite fields