Restricted enveloping algebras with minimal lie derived length

摘要

Let L be a non-abelian restricted Lie algebra over a field of characteristic p>0 and let u(L) denote its restricted enveloping algebra. In Siciliano (Publ Math (Debr) 68:503-513, 2006) it was proved that if u(L) is Lie solvable then the Lie derived length of u(L) is at least ?log_2(p+1)?. In the present paper we characterize the restricted enveloping algebras whose Lie derived length coincides with this lower bound.