arXiv subjects
Publications and source records attributed to Martin Mygind.
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 of $G$, i.e., $k[L^*]^G=k$. This property characterises the Cartan type algebras among the restricted simple Lie algebras.
Working over an algebraically closed field of characteristic p > 3, we calculate the orbit closures in the Witt algebra W under the action of its automorphism group G. We also outline how the same techniques can be used to determine closures of orbits of all heights except p-1 (in which case we only obtain a conditional statement) in the dual space W^* under the induced action of G. As a corollary we prove that the algebra of invariants k[W^*]^G is trivial.