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 $L^{\ast }$ under the coadjoint action of $G$, i.e., $k[L^{\ast }{]}^G=k$. This property characterises the Cartan type algebras among the restricted simple Lie algebras.

arXiv comment12 pages

References in corpus (1)

• Orbit Closures in the Witt Algebra and its Dual Space