Higher deformations of Lie algebra representations I

In the late 1980s, Friedlander and Parshall studied representations of a family algebras which were obtained as deformations distribution algebra first Frobenius kernel an algebraic group. The representation theory these tells us much about Lie in positive characteristic. We develop analogue this for higher kernels, answering 30 year old question posed by Parshall. also examine their case special linear