Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic number fields generated by Frobenius-Perron dimensions in
  fusion rings   From a unifying lemma concerning fusion rings, we prove a collection of
number-theoretic results about fusion, braided, and modular tensor categories.
First, we prove that every fusion ring has a dimensional grading by an
elementary abelian 2-group. As a result, we bound the order of the
multiplicative central charge of arbitrary modular tensor categories. We also
introduce Galois-invariant subgroups of the Witt group of nondegenerately
braided fusion categories corresponding to algebraic number fields generated by
Frobenius-Perron dimensions. Lastly, we provide a complete description of the
fields generated by the Frobenius-Perron dimensions of simple objects in
$\mathcal{C}(\mathfrak{g},k)$, the modular tensor categories arising from the
representation theory of quantum groups at roots of unity, as well as the
fields generated by their Verlinde eigenvalues.

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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex