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Outer Restricted Derivations Of Nilpotent Restricted Lie Algebras, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
Outer Restricted Derivations Of Nilpotent Restricted Lie Algebras, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
University Faculty and Staff Publications
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 …