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arXiv · 1002.0168

Non-cyclotomic fusion categories

Scott Morrison·Noah Snyder
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Abstract

Etingof, Nikshych and Ostrik ask in arXiv:math.QA/0203060 if every fusion category can be completely defined over a cyclotomic field. We show that this is not the case: in particular one of the fusion categories coming from the Haagerup subfactor arXiv:math.OA/9803044 and one coming from the newly constructed extended Haagerup subfactor arXiv:0909.4099 can not be completely defined over a cyclotomic field. On the other hand, we show that the double of the even part of the Haagerup subfactor is completely defined over a cyclotomic field. We identify the minimal field of definition for each of these fusion categories, compute the Galois groups, and identify their Galois conjugates.

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Scott Morrison, Noah Snyder. 2010-02-01. Non-cyclotomic fusion categories. https://doi.org/10.1090/s0002-9947-2012-05498-5

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