151. On the classification of simple Lie algebras of dimension seven over fields of characteristic 2
- Author
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Wilian Francisco de Araujo, Marinês Guerreiro, and Alexander Grishkov
- Subjects
Pure mathematics ,Rank (linear algebra) ,General Mathematics ,010102 general mathematics ,Dimension (graph theory) ,SUPERÁLGEBRAS DE LIE ,Field (mathematics) ,01 natural sciences ,010305 fluids & plasmas ,Computational Theory and Mathematics ,Simple (abstract algebra) ,0103 physical sciences ,Lie algebra ,0101 mathematics ,Statistics, Probability and Uncertainty ,Algebra over a field ,Algebraically closed field ,Mathematics - Abstract
This paper is the second part of paper (Grishkov and Guerreiro in Sao Paulo J Math Sci v4(1):93–107, 2010) about simple 7-dimensional Lie algebras over an algebraically closed field k of characteristic two. In this paper we prove that all simple 7-dimensional Lie algebras over k of absolute toral rank three are isomorphic to the Cartan algebra $$W_1$$ or the Hamilton algebra $$H_2.$$ We hope to prove that those algebras are the unique simple 7-dimensional Lie algebras over the field k. Observe that in the case of absolute toral rank 2 this fact was proved in [2].
- Published
- 2020