10-Commutators, 13-commutators and odd derivations

Askar Serkulovich Dzhumadil'daev

2008

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DOI 10.2991/jnmp.2008.15.1.7

Data confidence 70 medium

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Abstract

The anti-symmetric sumand does not vanish for some vector fields X 1 , . . ., X N .We construct 10-and 13-commutators on V ect(3) and 10-commutator on the space of divergence-free vector fields V ect 0 (3).We show that there are no other N -commutators on V ect(3) except for 2-, 10-and 13-commutators, and no other N -commutators on the Lie algebra of divergence-free vector fields V ect 0 (3) except for 2-, 10-commutators.These constructions are based on calculation of powers of odd derivations.