Non-cyclotomic fusion categories
Date
2012-04-17
Authors
Morrison, Scott
Snyder, Noah
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Publisher
American Mathematical Society
Abstract
Etingof, Nikshych and Ostrik asked 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 and one coming from the newly constructed extended Haagerup subfactor cannot be completely defined over a cyclotomic field. On the other hand, we show that the Drinfel'd center 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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Keywords
Fusion categories, cyclotomic fields, subfactors, counterexamples
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Transactions of the American Mathematical Society
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Journal article
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Open Access
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