Questions tagged [unitary-fusion-category]

Questions about fusion categories or tensor categories with a unitary (Hilbert space and dagger) structure on the morphisms, and dagger-preserving functors.

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19 votes
1 answer
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Is the representation category of quantum groups at root of unity visibly unitary?

Let $\mathfrak g$ be a simple Lie algebra. By taking the specialization at $q^\ell=1$ of a certain integral version¹ of the quantum group $U_q(\mathfrak g)$, and by considering a certain quotient ...
André Henriques's user avatar
14 votes
2 answers
694 views

Is a unitary Hamiltonian TQFT the same as a unitary axiomatic TQFT?

Introduction Axiomatic TQFTs An axiomatic $n$-dimensional TQFT is a symmetric monoidal functor $\mathcal{Z}\colon \operatorname{Bord}_n \to \operatorname{Hilb}$ from $n$-dimensional oriented ...
Manuel Bärenz's user avatar
9 votes
1 answer
337 views

Is there a simple argument that shows that two unitary fusion categories are Morita equivalent if their Drinfeld centers are equal?

By Morita equivalent I mean that there is an invertible bi-module between the two fusion categories. [Feel free to replace the Drinfeld centers being "equal" by an appropriate categorial notion of "...
Andi Bauer's user avatar
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