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 Togo 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 Gaschutz 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.

Autore Pugliese

• Siciliano Salvatore

Tutti gli autori

• J. FELDVOSS , S. SICILIANO , T. WEIGEL

Titolo volume/Rivista

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

Anno di pubblicazione

2013

ISSN

0002-9939

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

Non Disponibile

0

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile