Scheme Of Tori, Toral Stabilizer And Its Applications

In this thesis. We mainly investigate the scheme of tori, toral stabilizer of restricted Lie algebras over algebraically closed field of positive characteristic. The main contents are listed below:First, in chapter 3, we consider the restricted Lie algebra W(n). We obtain the Kostant’s differential criterion for the regular derivation. In chapter 4. we study the. scheme of tori and toral stabilizer, and establish a sufficient and neces-sary condition for the isomorphism between the Weyl group and toral stabilizer. Furthermore, for the Jacobson-Witt algebra, we describe all the Weyl groups and classify its semisimple orbits. Last, in chapter 5, we give a new description about the solvable restricted Lie algebra by using the toral stabilizer. Moreover, we discuss the subalgebra structure of classical Lie algebras.