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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.

RESTRICTED CARTAN TYPE LIE ALGEBRAS AND THE COADJOINT REPRESENTATION