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".
Best Answer
Some particular braided Hopf algebras known as Nichols algebras are useful in conformal field theories. Here you have some references:
Semikhatov, A. M.; Tipunin, I. Yu. Logarithmic $\widehat{s\ell}(2)$ CFT models from Nichols algebras: I. J. Phys. A 46 (2013), no. 49, 494011, 53 pp. MR3146017, arXiv
Semikhatov, A. M. Fusion in the entwined category of Yetter-Drinfeld modules of a rank-1 Nichols algebra. Russian version appears in Teoret. Mat. Fiz. 173 (2012), no. 1, 3–37. Theoret. and Math. Phys. 173 (2012), no. 1, 1329--1358. MR3171534, arXiv
Semikhatov, A. M.; Tipunin, I. Yu. The Nichols algebra of screenings. Commun. Contemp. Math. 14 (2012), no. 4, 1250029, 66 pp. MR2965674, arXiv
Added:
The abstract is the following: