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

• Carlos R. Payares Guevara ^[1] ; Fabián A. Arias Amaya ^[1]
  1. [1] Universidad Tecnológica de Bolívar

     Universidad Tecnológica de Bolívar

     Colombia

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 62, Nº. 1, 2021, págs. 123-139
• Idioma: inglés
• DOI: 10.33044/revuma.1555
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• Resumen

  • 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).