Outer restricted derivations of nilpotent restricted Lie algebras

Details Outer restricted derivations of nilpotent restricted Lie algebras Outer restricted derivations of nilpotent restricted Lie algebras

2011-02-13

arxiv.org/abs/1102.2629v2

Mathematics

Rings and Algebras

9 pages, minor revisions, to appear in Proc. Amer. Math. Soc

Scientific paper

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 T\^og\^o 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 Gasch\"utz 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.

Affiliated with

Also associated with

No associations

Rating

Outer restricted derivations of nilpotent restricted Lie algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Outer restricted derivations of nilpotent restricted Lie algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Outer restricted derivations of nilpotent restricted Lie algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-594