Nilpotent orbits of certain simple Lie algebras over truncated polynomial rings

Let F be an algebraically closed field of positive characteristic p> 3, and A the divided power algebra in one indeterminate, which, as a vector space, coincides with the truncated polynomial ring of F[T] by T^pn. Let g be the special derivation algebra over A which is a simple Lie algebra, and additionally non-restricted as long as n> 1. Let N be the nilpotent cone of g, and G=Aut(g), the automorphism group of g. In contrast with only finitely many nilpotent orbits in a classical simple Lie algebra, there are infinitely many nilpotent orbits in g. In this paper, we parameterize all nilpotent orbits, and obtain their dimensions. Furthermore, the nilpotent cone N is proven to be reducible and not normal. There are two irreducible components in N. The dimension of N is determined.