  In this article we construct a large family of $R$-matrices for various
extensions of small quantum groups by grouplike elements. The extensions are in
correspondence to lattices between root and weight lattice and admit
$R$-matrices in many cases where the original small quantum group does not. The
results of this work extends some results that are well-known for
$u_q(\mathfrak{sl}_2)$. Especially for $A_n$ a combinatorial theorem about
roots of unity was necessary, which is interesting on its own, and has been
proven in a separate paper [LN14].
