Fusion in the entwined category of Yetter–Drinfeld modules of a rank-1 Nichols algebra

In the braided context, we rederive a popular nonsemisimple fusion algebra from a Nichols algebra. Together with the decomposition that we find for the product of simple Yetter–Drinfeld modules, this strongly suggests that the relevant Nichols algebra furnishes an equivalence with the triplet $W$-algebra in the $(p,1)$ logarithmic models of conformal field theory. For this, the category of Yetter–Drinfeld modules is to be regarded as an entwined category (i.e., a category with monodromy but not with braiding).