Generalized Amitsur-Levitski theorem and equations for sheets in a reductive complex Lie algebra
arXiv:1309.7076
Abstract
I connect an old result of mine on a Lie algebra generalization of the Amitsur-Levitski theorem with equations for sheets in a reductive Lie algebra and with recent results of Kostant-Wallach on the variety of singular elements in a reductive Lie algebra.
17 pages, key words: Amitsur-Levitski theorem, invariant theory, polynomial identities, sheets, abelian ideals and solvable Lie algebras, representation theory, enveloping algebras, nilpotent cone, Lie algebra cohomology