Adjoint quotient maps for the restricted Lie algebras W-n and S-n

摘要

We give an explicit description of the adjoint quotient maps for the Jacobson-Witt algebra W-n and the special algebra S-n. An analog of Kostant's differential criterion of regularity is given for W-n. Furthermore, we describe the fiber of the adjoint quotient map for S-n and construct analogs of Kostant's transverse slice for W-n. In addition, we analyze nilpotent elements and generalize some of Premet's results (8) to S-n.