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N-commutators on vector fields

A. S. Dzhumadil'daev
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Abstract

An alternating sum of compositions of N vector fields is called N-commutator. In general N-commutator of N vector fields is no longer a vector field. Question: is it possible to find N=N(n), such that N-commutator of any vector fields in $Vect(n)$ is once again a vector field. Theorem: $n^2+2n-2$-commutator is a such one. A theory of N-commutators with emphasis on 5-and 6-commutators on two dimensional manifold is developed.

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BibTeXRIS

A. S. Dzhumadil'daev. 2002-03-18. N-commutators on vector fields. https://arxiv.org/abs/math/0203036

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