begin tl;dr: I just read this paper which gives the equations for the structure constants, braiding operators etc. for a generic quantum Lie algebra. I always found it very annoying that in the Kauffman abstract tensor formalism, you need caps and cups (read: creation and destruction operators, if you read it as Feynman diagrams), at least for undirected lines. Since in any graphical formalism (read: birdtracks - what I do since 30 years might be called quantum birdtracks), the "space" and "time" directions are equivalent. (OK, one could gauge in some left and right kink operators equal to cup and cap, but that's very artificial. But then, why should I be able to unify relativity and quantum theory :-)
Now these equations are even worse in that kind - when one writes the tensors graphically, even left-right symmetry is violated. Outside twistor theory, this is a no-no :-) Thus: Is there an equivalent formulation of quantum Lie algebras (as tensors) keeping as many symmetries as possible (as graphs)?
