On Lie solvable restricted enveloping algebras

In this note we study the Lie derived lengths of a restricted enveloping algebra u(L), for a non-abelian restricted Lie algebra L over a field of positive characteristic p. For p > 2 we show that if the Lie derived length of u(L) is minimal then u(L) is Lie nilpotent. Moreover, we investigate the case when the strong Lie derived length of u(L) is minimal. For odd p we establish a classification of Lie centrally metabelian restricted enveloping algebras. (c) 2007 Elsevier Inc. All rights reserved.