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arXiv · 2010.11872

Constructing non-semisimple modular categories with relative monoidal centers

Robert Laugwitz·Chelsea Walton
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Abstract

This paper is a contribution to the construction of non-semisimple modular categories. We establish when M\"uger centralizers inside non-semisimple modular categories are also modular. As a consequence, we obtain conditions under which relative monoidal centers give (non-semisimple) modular categories, and we also show that examples include representation categories of small quantum groups. We further derive conditions under which representations of more general quantum groups, braided Drinfeld doubles of Nichols algebras of diagonal type, give (non-semisimple) modular categories.

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Robert Laugwitz, Chelsea Walton. 2020-10-22. Constructing non-semisimple modular categories with relative monoidal centers. https://doi.org/10.1093/imrn%2Frnab097

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