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

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    Abstract

    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.
    Original languageEnglish
    Pages (from-to)833–884
    Number of pages32
    JournalAdvances in Mathematics
    Volume311
    Early online date5 Apr 2017
    DOIs
    Publication statusPublished - Apr 2017

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