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

Alexandre Premet (Manchester)

Frank Adams 1,

I will talk on the joint work with David Stewart where we use earlier results of Dynkin, Seitz, Testerman and Liebeck-Seitz on maximal connected subgroups of simple algebraic groups G to describe the conjugacy classes of maximal subalgebras of the Lie algebra \(Lie(G)\). In positive characteristic, not all maximal subalgebras of \(Lie(G)\) have form \(Lie(H)\) for some maximal connected subgroup \(H\) of \(G\). A complete answer is obtained in the case where \(G\) is an exceptional simple algebraic group defined over an algebraically closed field of characteristic \(p\), where \(p\) is a good prime for the root system of \(G\) (this means that \(p>3\) if \(G\) is of type \(G2\), \(F4\), \(E6\), \(E7\) and \(p>5\) of \(G\) is of type \(E8\)).

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