A link to the page is available here. The relevant bit is on P. 15 of the book. I would really appreciate it if somebody could help! It is probably something quite obvious, hence left out by the author, but I don't seem to see it!
Could someone please explain the following I've read in Solitons, Instantons and Twistors. (I have changed the notation a bit -- I am more used to $"i,j,k"$)
$\xi_i$ are coordinates, with $i=1,...,2n$
Suppose $w^{ij}$ is an invertible, antisymmetric matrix
Define $\{f,g\}:=\sum_{i,j=1}^{2n} w^{ij}(\xi){\partial f\over \partial \xi_i}{\partial g\over \partial \xi_j}$ and it satisfies $\{a,\{b,c\}\}+\{b,\{c,a\}\}+\{c,\{a,b\}\}=0$
Let $W_{ij}:=(w^{-1})_{ij}$ Why is it that it follows that ${\partial W_{jk}\over \partial \xi_i}+{\partial W_{ki}\over \partial \xi_j}+{\partial W_{ij}\over \partial \xi_k}=0,\,\,\,\,\,\forall i,j,k=1,...,2n$?
It is also said that $w^{ij}(\xi)=\{\xi^i,\xi^j\}$
Thank you.
Please help!