Payares Guevara, Carlos R. y Fabián A. Arias Amaya. "Classical simple Lie 2-algebras of odd toral rank and a contragredient Lie 2-algebra of toral rank 4" Revista de La Unión Matemática Argentina , vol. 62, no. 1, 29 de abril de 2021, págs. 123-139, https://doi.org/10.33044/revuma.1555.
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After the classification of simple Lie algebras over a field of characteristic p > 3, the main problem not yet solved in the theory of finite dimensional Lie algebras is the classification of simple Lie algebras over a field of characteristic 2. The first result for this classification problem ensures that all finite dimensional Lie algebras of absolute toral rank 1 over an algebraically closed field of characteristic 2 are soluble. Describing simple Lie algebras (respectively, Lie 2-algebras) of finite dimension of absolute toral rank (respectively, toral rank) 3 over an algebraically closed field of characteristic 2 is still an open problem. In this paper we show that there are no classical type simple Lie 2-algebras with toral rank odd and furthermore that the simple contragredient Lie 2-algebra G(F4,a) of dimension 34 has toral rank 4. Additionally, we give the Cartan decomposition of G(F4,a).
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