Some particular braided Hopf algebras known as [Nichols algebras][1] 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][2]
- 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][3]
- Semikhatov, A. M.; Tipunin, I. Yu. The Nichols algebra of screenings. Commun. Contemp. Math. 14 (2012), no. 4, 1250029, 66 pp. MR2965674, [arXiv][4]
**Added**:
- Lentner, S. Quantum groups and Nichols algebras acting on conformal field theories, [arXiv][5]
The abstract is the following:
> We prove a long-standing conjecture by B. Feigin et al. that certain
> screening operators on a conformal field theory obey the algebra
> relations of the Borel part of a quantum group (and more generally a
> diagonal Nichols algebra). Up to now this has been proven only for the
> quantum group $u_q(\mathfrak{sl}_2)$. The proof is based on a novel,
> intimate relation between Hopf algebras, Vertex algebras and a class
> of analytic functions in several variables, which are generalizations
> of Selberg integrals. These special functions have zeroes wherever the
> associated diagonal Nichols algebra has a relation, because we can
> prove analytically a quantum symmetrizer formula for them. Morevover,
> we can use the poles of these functions to construct a crucial Weyl
> group action. Our result produces an infinite-dimensional graded
> representation of any quantum group or Nichols algebra. We discuss
> applications of this representation to Kazhdan-Lusztig theory.
[1]: https://en.wikipedia.org/wiki/Nichols_algebra
[2]: http://arxiv.org/abs/1301.2235
[3]: http://arxiv.org/abs/1109.5919
[4]: http://arxiv.org/abs/1101.5810
[5]: https://arxiv.org/abs/1702.06431