It is well-known, that there are a lot of applications of classical Hopf algebras in QFT, e.g. Connes-Kreimer renormalization, Birkhoff decomposition, Zimmermann formula, properties of Rota-Baxter algebras, Hochschild cohomology, Cartier-Quillen cohomology, motivic Galois theory etc.

But all these structures are based on Hopf algebras in monoidal categories with trivial braiding, e.g. given by $\tau(a\otimes b)=b\otimes a$.

Are there some applications of braided Hopf algebras in QFT ? I'm looking for some examples which are both nontrivial and "calculable".

It is well-known, that there are a lot of applications of classical Hopf algebras in QFT, e.g. Connes-Kreimer renormalization, Birkhoff decomposition, Zimmermann formula, properties of Rota-Baxter algebras, Hochschild cohomology, Cartier-Quillen cohomology, motivic Galois theory etc.

But all these structures are based on Hopf algebras in monoidal categories with trivial braiding, e.g. given by $\tau(a\otimes b)=b\otimes a$.

Are there some applications of braided Hopf algebras (i.e. an object in some braided monoidal category) in QFT ? I'm looking for some examples which are both nontrivial and "calculable".