Let $(H, m, \Delta, u, \epsilon, S, R)$ be a quasi-triangular Hopf algebra, where $H$ is a (finite-dimensional) vector space over a field $\mathbb{K}$ with the structure maps $m: H \otimes H \rightarrow H$, $\Delta: H \rightarrow H \otimes H$, $u: \mathbb{K} \rightarrow H$, $\epsilon: H \rightarrow \mathbb{K}$, $S: H \rightarrow H$, and an invertible element $R \in H \otimes H$, satisfying certain equations.
A ribbon Hopf algebra is a quasi-triangular Hopf algebra with an invertible central element $r$, satisfying the following conditions:
$r^{2}=uS(u)$, $S(r)=r$, $\epsilon(r)=1$,
$\Delta(r)=(R_{21}R_{12})^{-1}(r \otimes r)$,
where $u=m(S \otimes id)(R_{21})$ is the so-called Drinfeld element.
The main source of examples of ribbon Hopf algebras are the quantum groups e.g. $U_{q}(sl_{2})$. The other examples is the quantum double $D(H)$ of a Hopf algebra. Are there other "nice" examples of ribbon Hopf algebras? Thank you in advance.