So I am doing some algebra calculations with what I thought were Lie Algebras.   It looks like

Hello,

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:

f^{0ij}_{\rho}*f^{\sigma\alpha\rho}_{\beta}=f^{\sigma\alpha0}_{\rho}*f^{\rhoij}_{\beta}+f^{\sigma\alphai}_{\rho}*f^{0\rhok}_{\beta}+f^{\sigma\alphaj}_{\rho}*f^{0i\rho}_{\beta}