Nilpotent fusion categories
نویسندگان
چکیده
منابع مشابه
Fusion Categories Of
We classify semisimple rigid monoidal categories with two iso-morphism classes of simple objects over the field of complex numbers. In the appendix written by P. Etingof it is proved that the number of semisimple Hopf algebras with a given finite number of irreducible representations is finite.
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Etingof, Nikshych and Ostrik ask in [8, §2] 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 [2] and one coming from the newly constructed extended Haagerup subfactor [3] can not be completely defined over a cyclotomic field. On the other hand, we show that...
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Dimensions of objects in fusion categories are cyclotomic integers, hence number theoretic results have implications in the study of fusion categories and finite depth subfactors. We give two such applications. The first application is determining a complete list of numbers in the interval (2, 76/33) which can occur as the FrobeniusPerron dimension of an object in a fusion category. The smalles...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2008
ISSN: 0001-8708
DOI: 10.1016/j.aim.2007.08.001