On simple Lie 2-algebra of toral rank 3

2019/02/28 by Guevara, Carlos Rafael Payares, Acevedo, Jeovanny de Jesus Muentes
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1903.00057

Abstract

Simple Lie algebras of finite dimension over an algebraically closed field of characteristic 0 or p> 3 were recently classified. However, the problem over an algebraically closed field of characteristics 2 or 3 there exist only partial results. The first result on the problem of classification of simple Lie algebra of finite dimension over an algebraically closed field of characteristic 2 is that these algebras have absolute toral rank greater than or equal to 2. In this paper we show that there are not simple Lie 2-algebras with toral rank 3 over an algebraically closed field of characteristic 2 and dimension less or equal to 16.

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• Lie 2-algebras of toral rank 3
• Classical simple Lie 2-algebras of toral rank 3 and a contragredient Lie 2-algebra of toral rank 4
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