A modular analogue of Morozov's theorem on maximal subalgebras of simple Lie algebras

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Let G be a simple algebraic group over an algebraically closed eld of characteristic p > 0 and suppose that p is a very good prime for G. In this paper we prove that any maximal Lie subalgebra M of g = Lie(G) with rad(M) 6= 0 has the form M = Lie(P) for some maximal parabolic subgroup P of G. This means that Morozov's theorem on maximal subalgebras is valid under mild assumptions on G. We show that such assumptions are necessary by providing a counterexample to Morozov's theorem for groups of type E8 over elds of characteristic 5. Our proof relies on the main results and methods of the classication theory of nite dimensional simple Lie algebras over elds of prime characteristic.

Bibliographical metadata

Original languageEnglish
Pages (from-to)833–884
Number of pages32
JournalAdvances in Mathematics
Early online date5 Apr 2017
Publication statusPublished - Apr 2017

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