XXV Workshop on Geometric Methods in Physics | 2-8.07.2006 | |||||

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## Askar Dzhumadil'daev## N-commutators and identitiesA commutator $[X,Y]=XY-YX$ is a well-known tensor operation on a space of vector fields $Vect(n).$ We construct new tensor operation on $Vect(n).$ Namely, we establish that $N$-ary skew-symmetric sum of $N$ compositions by all permutations is a well-defined operation if $N=n^2+2n-2.$ References. 1.A.S. Dzhumadil'daev, {\em $N$-commutators,} Comment Math Helv, 79(2004), 516-553. 2. A.S. Dzhumadil'daev, {\em 10-commutator and 13-commutator,} Preprint MPIM, Bonn, 2006. |