Unitarizability of premodular categories. (English) Zbl 1184.17007
Summary: We study the unitarizability of premodular categories constructed from representations of quantum group at roots of unity. We introduce Grothendieck unitarizability as a natural generalization of unitarizability to classes of premodular categories with a common Grothendieck semiring. We obtain new results for quantum groups of Lie types \(F_4\) and \(G_2\), and improve the previously obtained results for Lie types \(B\) and \(C\).
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 18D10 | Monoidal, symmetric monoidal and braided categories (MSC2010) |
| 20G42 | Quantum groups (quantized function algebras) and their representations |
Keywords:
premodular category; ribbon fusion category; semisimple complex-linear ribbon category; finitely many isomorphism classes of simple objects; Frobenius-Perron dimension; Grothendieck unitarizability; quantum groups of Lie typesReferences:
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