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Creators/Authors contains: "Bruillard, Paul"

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  1. ; ; ; (, Journal of Algebra and Its Applications)
    null (Ed.)
    We develop categorical and number-theoretical tools for the classification of super-modular categories. We apply these tools to obtain a partial classification of super-modular categories of rank [Formula: see text]. In particular we find three distinct families of prime categories in rank [Formula: see text] in contrast to the lower rank cases for which there is only one such family. 
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  2. ; ; (, Proceedings of the American Mathematical Society)
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  3. ; ; ; ; ; (, Algebras and Representation Theory)
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  4. ; ; ; (, Journal of the American Mathematical Society)
    null (Ed.)
    We prove a rank-finiteness conjecture for modular categories: up to equivalence, there are only finitely many modular categories of any fixed rank. Our technical advance is a generalization of the Cauchy theorem in group theory to the context of spherical fusion categories. For a modular category C \mathcal {C} with N = ord ( T ) N= \textrm {ord}(T) , the order of the modular T T -matrix, the Cauchy theorem says that the set of primes dividing the global quantum dimension D 2 D^2 in the Dedekind domain Z [ e 2 π i N ] \mathbb {Z}[e^{\frac {2\pi i}{N}}] is identical to that of N N . 
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