Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Classification of Modular Fusion Algebras   We introduce the notion of (nondegenerate) strong-modular fusion algebras.
Here strongly-modular means that the fusion algebra is induced via Verlinde's
formula by a representation of the modular group SL(2,Z) whose kernel contains
a congruence subgroup. Furthermore, nondegenerate means that the conformal
dimensions of possibly underlying rational conformal field theories do not
differ by integers. Our main result is the classification of all
strongly-modular fusion algebras of dimension two, three and four and the
classification of all nondegenerate strongly-modular fusion algebras of
dimension less than 24. We use the classification of the irreducible
representations of the finite groups SL(2,Z_{p^l}) where p is a prime and l a
positive integer. Finally, we give polynomial realizations and fusion graphs
for all simple nondegenerate strongly-modular fusion algebras of dimension less
than 24.

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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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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: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys