A modular analogue of Morozov%26apos;s theorem on maximal subalgebras of simple Lie algebras

作者：Premet Alexander

来源：Advances in Mathematics, 2017, 311: 833-884.

DOI：10.1016/j.aim.2017.03.011

• Simple algebraic groups
• Modular Lie algebras
• Maximal subalgebras

Let G be a simple algebraic group over an algebraically closed field 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) not equal 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 E-8 over fields of characteristic 5. Our proof relies on the main results and methods of the classification theory of finite dimensional simple Lie algebras over fields of prime characteristic.

• 出版日期2017-4-30