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

Lookup NU author(s): Dr David Stewart

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This is the authors' accepted manuscript of an article that has been published in its final definitive form by American Mathematical Society, 2019.

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Abstract

Let G be an exceptional simple algebraic group over an algebraically closed field k and suppose that p = char(k) is a good prime for G. In this paper we classify the maximal Lie subalgebras m of the Lie algebra g = Lie(G). Specifically, we show that either m = Lie(M) for some maximal connected subgroup M of G or m is a maximal Witt subalgebra of g or m is a maximal exotic semidirect product. The conjugacy classes of maximal connected subgroups of G are known thanks to the work of Seitz, Testerman and Liebeck–Seitz. All maximal Witt subalgebras of g are G-conjugate and they occur when G is not of type E6 and p − 1 coincides with the Coxeter number of G. We show that there are two conjugacy classes of maximal exotic semidirect products in g, one in characteristic 5 and one in characteristic 7, and both occur when G is a group of type E7.


Publication metadata

Author(s): Premet A, Stewart DI

Publication type: Article

Publication status: Published

Journal: Journal of the American Mathematical Society

Year: 2019

Volume: 32

Pages: 965-1008

Online publication date: 19/07/2019

Acceptance date: 24/04/2019

Date deposited: 26/04/2019

ISSN (print): 0894-0347

ISSN (electronic): 1088-6834

Publisher: American Mathematical Society

URL: https://doi.org/10.1090/jams/926

DOI: 10.1090/jams/926


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