XXV Workshop on Geometric Methods in Physics 2-8.07.2006

Askar Dzhumadil'daev

N-commutators and identities

A 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 $N=n^2+2n-2.$

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.