Seminar

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A braided finite tensor category is called modular if it is nondegenerate and ribbon. 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. In this talk, we will discuss 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 the semisimple case. We discuss small quantum groups $u_q(sl_2)$ and the Drinfeld doubles of Nichols Hopf algebras, especially the $\mathrm{SL}(2, \mathbb{Z})$-representation on their centers, Cohen-Westreich modular data, and the validity of the congruence kernel theorem.

Modular Data of Non-Semisimple Modular Categories