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 S-matrix diagonalizes the mixed fusion rules and reduces to the usual S-matrix for semisimple modular categories. The paper includes detailed studies on small quantum groups U_qsl(2) and the Drinfeld doubles of Nichols Hopf algebras, especially the SL(2, ℤ)-representation on their centers, Cohen-Westreich modular data, and the congruence kernel theorem's validity.