Uniqueness of unitary structure for unitarizable fusion categories

DOI10.1007/S00220-022-04425-7arXiv1906.09710MaRDI QIDQ6320925

Publication date: 23 June 2019

Abstract: We show that every unitarizable fusion category, and more generally every semisimple C*-tensor category, admits a unique unitary structure. Our proof is based on a categorified polar decomposition theorem for monoidal equivalences between such categories. We prove analogous results for unitarizable braided fusion categories and module categories.

Mathematics Subject Classification ID

Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Fusion categories, modular tensor categories, modular functors (18M20) Dagger categories, categorical quantum mechanics (18M40)

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