I have been reading some reviews and looked into books on anyons and topological quantum computation and I found it a little difficult to make out a short list of parameters and a clear and short list of mathematical structures needed to define an anyonic system. I would like to ask for help here. In Nayak et al.'s review I found the following list and would like to know, whether it is complete:
- particle species
- fusion rules
- F-matrix for recoupling of the anyonic charges
- R-matrix for the braiding
- topological spins
For the maths structure, one needs a ribbon fusion category. Is this enough? And that about the spin is associated to $SO(2)$? Do I need to add a statement about that also into the list?