Document Type

Article

Publication Title

Proceedings of the American Mathematical Society

Abstract

In this paper we prove that every finite-dimensional nilpotent restricted Lie algebra over a field of prime characteristic has an outer restricted derivation whose square is zero unless the restricted Lie algebra is a torus or it is one-dimensional or it is isomorphic to the three-dimensional Heisenberg algebra in characteristic two as an ordinary Lie algebra. This result is the restricted analogue of a result of Tôgô on the existence of nilpotent outer derivations of ordinary nilpotent Lie algebras in arbitrary characteristic and the Lie-theoretic analogue of a classical group-theoretic result of Gaschütz on the existence of p-power automorphisms of p-groups. As a consequence we obtain that every finite-dimensional non-toral nilpotent restricted Lie algebra has an outer restricted derivation.

First Page

171

Last Page

179

DOI

https://doi.org/10.1090/S0002-9939-2012-11316-4

Publication Date

2012

Department

Mathematics and Statistics

Comments

This is the pre-print version of this article. The published version can be found at the following link: https://www.ams.org/journals/proc/2013-141-01/S0002-9939-2012-11316-4/ or https://doi.org/10.1090/S0002-9939-2012-11316-4.

This article is licensed under the following Creative Commons licenses: CC-BY-NC Attribution-NonCommercial 4.0 International and CC-BY-NC-ND Attribution-NonCommercial 4.0 International

Download

Share

COinS