Quote by George Jones
Are you working with real or complex Lie algebras?

Apologies George  I should have said, the Lie Algebras are complex. Any hints (however vague) would be much appreciated. :)
Quote by matt grime
Have you considered that there might be more than one basis you can think of?

Hmmm, ok  so at the moment I'm considering a basis of [tex]\mathfrak{so}(4)[/tex] of the form:
[tex]\left{\left(\begin{array}{cccc}0&1&0&0\\1&0&0&0\\0&0&0&0\\0&0&0&0\end{array}\right), \left(\begin{array}{cccc}0&0&1&0\\0&0&0&0\\1&0&0&0\\0&0&0&0\end{array}\right), \quad \textrm{etc.}\right}[/tex]
But perhaps if I think about suitable combinations of these, I'll get something more like the form I'm looking for?
The help is much appreciated guys. :)