Question: Solve this tensor equation


I have what may or may not be a nasty equation for the structure constants of a particular algebra I would like to classify.  Said equation looks like:




roman indices scroll from 1 to 3.  greek indices scroll from 0 to 3.  All the f's are completely antisymmetric in the upstairs indices.  And my constraints are:  F^{ijk}_{l}=0, and f^{ijk}_{0}=\epsilon^{ijk}.  And, I am implicitly summing over \rho.


Is there a clever way to do this with maple{ I hope!}.  I attempted to write out all combinations by hand, and arrived at 64 equations.  Some of those were redundant and that cut the number down to 24.  Taking in to account antisymmetry when I tried to translate this into single variables to solve, I get an inconsistent system.  As I am certaintly not clever enough to do this error fre,  Any help at all would probably make my entire year!  Thanks so much

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