Maximal subalgebras of Cartan type in the exceptional Lie algebras

摘要

In this paper we initiate the study of the maximal subalgebras of exceptionalsimple classical Lie algebras \g over algebraically closed fields k of positivecharacteristic p, such that the prime characteristic is good for \g. In thispaper we deal with what is surely the most unnatural case; that is, where themaximal subalgebra in question is a simple subalgebra of non-classical type. Weshow that only the first Witt algebra can occur as a subalgebra of \g and giveexplicit details on when it may be maximal in \g.