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