Year: 2024
Type: article
Abstract: 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.
Authors: Liang Chang, Quinn T. Kolt, Zhenghan Wang, Qing Zhang
Institutions: Nankai University, University of California, Santa Barbara
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405649882