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Non-cyclotomic fusion categories

Authors: Scott Morrison and Noah Snyder
Journal: Trans. Amer. Math. Soc. 364 (2012), 4713-4733
MSC (2010): Primary 18D10; Secondary 46L37
Published electronically: April 17, 2012
MathSciNet review: 2922607
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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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Additional Information

Scott Morrison
Affiliation: Miller Institute for Basic Research, University of California at Berkeley, Berkeley, California 94720

Noah Snyder
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027

Keywords: Fusion categories, cyclotomic fields, subfactors, counterexamples
Received by editor(s): October 1, 2010
Published electronically: April 17, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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