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I'm a physicist and not yet an expert in fusion category. I've heard that it's possible to reconstruct a weak Hopf algebra from its category of representations, and would like to know how this works ...

By looking at defining relations of standard deformation of $\mathfrak{sl}_2$, which are: $$ [E,F] = \frac{q^{H}-q^{-H}}{q-q^{-1}}, \quad [H,E] = 2E, \quad \text{ and } \quad [H,F] = -2F, $$ some ...

As is well known, every compact quantum group in the sense of Woronowicz has a dense Hopf $*$-sub-algebra. For the case of $q-SU(n)$ (among others) this Hopf $*$-sub-algebra is an FRT-algebra, which ...