Maximal Lie subalgebras among locally nilpotent derivations

We study maximal Lie subalgebras among locally nilpotent derivations of the polynomial algebra. Freudenburg conjectured that the triangular Lie algebra of locally nilpotent derivations of the polynomial algebra is a maximal Lie algebra contained in the set of locally nilpotent derivations, and that every maximal Lie algebra contained in the set of locally nilpotent derivations is conjugate to the triangular Lie algebra. In this paper we prove the first part of the conjecture and present a counterexample to the second part. We also show that under a certain natural condition imposed on a maximal Lie algebra there is a conjugation taking this Lie algebra to the triangular Lie algebra. Bibliography: 2 titles.

polynomial algebra, Lie algebra, locally nilpotent derivation