| The Lie algebra associated to an affine group scheme over a field of positive characteristic p is naturally equipped with a p-operation. In other words, it is naturally a restricted or p-Lie algebra. Moreover, this restricted Lie algebra is closely related to the first Frobenius kernel of the group scheme. In the first part of the talk, I will review these classical constructions. In the second part, I will concentrate on finite group schemes. In particular, I will show that a simple finite group scheme over an algebraically closed field of positive characteristic p corresponds either to a simple (abstract) finite group or to a simple Lie algebra. Both these simple objects have been classified (the latter ones only in the case that p is different from 2 and 3). If time permits, I will discuss the deformations of these simple finite group schemes. |