Non-cyclotomic fusion categories
Quantum Algebra
2015-09-03 v2 Number Theory
Operator Algebras
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.
Cite
@article{arxiv.1002.0168,
title = {Non-cyclotomic fusion categories},
author = {Scott Morrison and Noah Snyder},
journal= {arXiv preprint arXiv:1002.0168},
year = {2015}
}
Comments
22 pages; improved version of Section 5