Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 18D10, 46L37

Retrieve articles in all journals with MSC (2010): 18D10, 46L37


Additional Information

Scott Morrison
Affiliation: Miller Institute for Basic Research, University of California at Berkeley, Berkeley, California 94720
Email: scott@tqft.net

Noah Snyder
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: nsnyder@math.columbia.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05498-5
PII: S 0002-9947(2012)05498-5
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.