Classification of finite dimensional simple Lie algebras in prime characteristics

Alexander Premet; Helmut Strade

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Classification of finite dimensional simple Lie algebras in prime characteristics

Alexander Premet·Helmut Strade

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Abstract

We give a comprehensive survey of the theory of finite dimensional Lie algebras over an algebraically closed field of characteristic p>0 and announce that for p>3 the classification of finite dimensional simple Lie algebras is complete. Any such Lie algebra is up to isomorphism either classical (i.e. comes from characteristic 0) or a filtered Lie algebra of Cartan type or a Melikian algebra of characteristic 5.

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Alexander Premet, Helmut Strade. 2006-03-07. Classification of finite dimensional simple Lie algebras in prime characteristics. https://arxiv.org/abs/math/0601380

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