English

Periodic derivations and prederivations of Lie algebras

Rings and Algebras 2011-08-18 v1

Abstract

We consider finite-dimensional complex Lie algebras admitting a periodic derivation, i.e., a nonsingular derivation which has finite multiplicative order. We show that such Lie algebras are at most two-step nilpotent and give several characterizations, such as the existence of gradings by sixth roots of unity, or the existence of a nonsingular derivation whose inverse is again a derivation. We also obtain results on the existence of periodic prederivations. In this context we study a generalization of Engel-4-Lie algebras.

Keywords

Cite

@article{arxiv.1108.3548,
  title  = {Periodic derivations and prederivations of Lie algebras},
  author = {D. Burde and W. Moens},
  journal= {arXiv preprint arXiv:1108.3548},
  year   = {2011}
}