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arXiv · 1108.3548

Periodic derivations and prederivations of Lie algebras

D. Burde·W. Moens
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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.

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D. Burde, W. Moens. 2011-08-17. Periodic derivations and prederivations of Lie algebras. https://arxiv.org/abs/1108.3548

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