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 Gaschuetz 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

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 [10.1090/S0002-9939-2012-11316-4].

Outer restricted derivations of nilpotent restricted Lie algebras

Weigel, T
2013

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 Gaschuetz 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
Articolo in rivista - Articolo scientifico
restricted derivations, restricted Lie algebras
English
2013
141
1
171
179
open
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 [10.1090/S0002-9939-2012-11316-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/49066
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