Restricted Cartan Type Lie Algebras and the Coadjoint Representation

Abstract

Let L be a restricted Cartan type Lie algebra over an algebraically closed field k of characteristic p > 3, and let G denote the automorphism group of L. We prove that there are no nontrivial invariants of L * under the coadjoint action, i.e., k[L * ] G = k. This property characterises the Cartan type algebras among the restricted simple Lie algebras.