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
Recommended Citation
Feldvoss, J., Siciliano, S., & Weigel, T. (2013). Outer restricted derivations of nilpotent restricted Lie algebras. Proceedings of the American Mathematical Society, 141(1), 171-179.
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