Classification of the maximal subalgebras of exceptional Lie algebras over fields of good characteristic

Alexander Premet; David Stewart

doi:10.1090/jams/926

Classification of the maximal subalgebras of exceptional Lie algebras over fields of good characteristic

Alexander Premet, David Stewart

Pure Mathematics

Newcastle University

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Abstract

Let G be an exceptional simple algebraic group over an algebraically closed field of characteristic p>0 and let g be the Lie algebra of G. Suppose further that p is a good prime for the root system of G. In this paper we classify all maximal Lie subalgebras of the Lie algebra g. This extends classical results of Dynkin from 1950s to simple Lie algebras over fields of positive characteristics.

Original language	English
Pages (from-to)	965-1008
Number of pages	44
Journal	Journal of the American Mathematical Society
Volume	32
Issue number	4
Early online date	19 Jul 2019
DOIs	https://doi.org/10.1090/jams/926
Publication status	Published - 1 Oct 2019

Keywords

exceptional groups, exceptional Lie algebras, maximal subalgebras

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10.1090/jams/926

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AB - Let G be an exceptional simple algebraic group over an algebraically closed field of characteristic p>0 and let g be the Lie algebra of G. Suppose further that p is a good prime for the root system of G. In this paper we classify all maximal Lie subalgebras of the Lie algebra g. This extends classical results of Dynkin from 1950s to simple Lie algebras over fields of positive characteristics.

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Classification of the maximal subalgebras of exceptional Lie algebras over fields of good characteristic

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