Braid group representations from twisted quantum doubles of finite groups. (English) Zbl 1207.16038
Summary: We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite groups, in contrast to the categories associated with quantum groups at roots of unity. We also show that in the case of \(p\)-groups, the corresponding pure braid group representations factor through a finite \(p\)-group, which answers a question asked to the first author by V. Drinfeld.
MSC:
16T20 | Ring-theoretic aspects of quantum groups |
20F36 | Braid groups; Artin groups |
18D10 | Monoidal, symmetric monoidal and braided categories (MSC2010) |
20C15 | Ordinary representations and characters |