The Classification Of F-stable Three Dimensional Subalgebras Of Simple Lie Algebras Of Exceptional Type

In this paper, we try to discuss the structure theory of classical simple Lie algebras (corresponding to simple algebraic groups) which under the action of Frobenius Lie morphism (over an algebraically closed field of characteristic p > 0). There are two parts of our result. The first part, We show the Frobenius Lie morphism on classical simple Lie algebra which is directly set up on the Lie algebra itself (introduced by Du-Shu, cf [6])is consistent with the induced action on Lie algebras from the Frobenius map on corresponding simple algebraic groups (cf [14]). The second part, We obtain the classifications of the three dimensional simple Lie subalgebras which keep stable under the action of Frobenius Lie morphism of classical simple algebras of exceptional type.