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

TL;DR

This paper investigates the deformations of current Lie algebras over a 3-dimensional simple algebra in characteristic 2, providing classification results for certain simple Lie algebras based on cohomology computations.

Contribution

It computes low-degree cohomology of current Lie algebras in characteristic 2 and applies these results to classify specific simple Lie algebras.

Findings

Computed low-degree cohomology of current Lie algebras in characteristic 2

Determined deformations of related semisimple Lie algebras

Classified simple Lie algebras of absolute toral rank 2 with specific Cartan subalgebra properties

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.