Modular data of non-semisimple modular categories

We investigate non-semisimple modular categories with an eye towards a structure theory, low-rank classification and applications to low dimensional topology and topological physics. We aim to extend the well-understood theory of semisimple modular categories to the non-semisimple case by using representations of factorizable ribbon Hopf algebras as a case study. We focus on the Cohen–Westreich modular data, which is obtained from the Lyubashenko–Majid modular representation restricted to the Higman ideal of a factorizable ribbon Hopf algebra. The Cohen–Westreich [Formula: see text]-matrix diagonalizes the mixed fusion rules and reduces to the usual [Formula: see text]-matrix for semisimple modular categories. The paper includes detailed studies on small quantum groups [Formula: see text] and the Drinfeld doubles of Nichols Hopf algebras, especially the [Formula: see text]-representation on their centers, Cohen–Westreich modular data, and the congruence kernel theorem’s validity.