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# 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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### Monoidal class vs gauge class vs Grothendieck class

In the comments under this post, three notions of equivalence classes of unitary modular tensor categories are brought up. They are monoidal classes, gauge classes, and Grothendieck class. Could ...
• 141
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### Are there interesting examples of unitary fusion categories where a tensor product of two simple objects is simple?

Let $\mathcal{C}$ be a unitary fusion category. Is it true that the tensor product of any two simple objects is simple ? If not, are there interesting (nontrivial) examples of such a $\mathcal{C}$ ?
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### Is an integral fusion category pseudo-unitary over a finite field?

Here are two propositions in the book Tensor Categories: Proposition 9.5.1. A pseudo-unitary fusion category admits a unique spherical structure. Proposition 9.6.5. Let $\mathcal{C}$ be ...
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10 votes
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### Is there a fusion category not Grothendieck equivalent to a unitary one?

We refer to the book Tensor categories by Etingof-Gelaki-Nikshych-Ostrik (MR3242743) for the notion of (unitary) fusion category. Two fusion categories are Grothendieck equivalent if they have the ...
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3 votes
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### Extended cyclotomic criterion for unitary categorification

According to this paper (Corollary 8.54) the Frobenius-Perron dimension (FPdim) of any object $a$ of a fusion category over $\mathbb{C}$ is a cyclotomic integer. Now, FPdim($a$) is the maximal ...
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2 votes
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103 views

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