Lie solvable enveloping algebras of characteristic two

TL;DR

This paper completes the classification of Lie solvable restricted enveloping algebras by resolving the characteristic 2 case, and characterizes Lie algebras with Lie solvable enveloping algebras over any field.

Contribution

It provides the missing classification for characteristic 2 and extends the characterization of Lie algebras with Lie solvable enveloping algebras to all fields.

Findings

Resolved the classification of Lie solvable restricted enveloping algebras in characteristic 2.

Characterized Lie algebras over any field with Lie solvable enveloping algebras.

Abstract

Lie solvable restricted enveloping algebras were characterized by Riley and Shalev except when the ground field is of characteristic 2. We resolve the characteristic 2 case here which completes the classification. As an application of our result, we obtain a characterization of ordinary Lie algebras over any field whose enveloping algebra is Lie solvable.