Fusion categories containing a fusion subcategory with maximal rank
نویسندگان
چکیده
In this paper, we study fusion categories which contain a proper subcategory with maximal rank. They can be viewed as generalizations of near-group categories. We first prove that they admit spherical structure. then classify those are non-degenerate or symmetric. Finally, such rank 4.
منابع مشابه
ABELIAN CATEGORIES ARISING FROM A MAXIMAL n-ORTHOGONAL SUBCATEGORY
As Koenig and Zhu showed, quotient of a triangulated category by a maximal 1-orthogonal subcategory becomes an abelian category. In this paper, we generalize this result to a maximal n-orthogonal subcategory for an arbitrary positive integer n.
متن کاملFusion 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.
متن کاملNon-cyclotomic Fusion Categories
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...
متن کاملA Finiteness Property for Braided Fusion Categories
We introduce a finiteness property for braided fusion categories, describe a conjecture that would characterize categories possessing this, and verify the conjecture in a number of important cases. In particular we say a category has property F if the associated braid group representations factor over a finite group, and suggest that categories of integral Frobenius-Perron dimension are precise...
متن کامل2 2 A ug 2 01 7 MORITA EQUIVALENCE OF POINTED FUSION CATEGORIES OF SMALL RANK
We classify pointed fusion categories C(G,ω) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2, 2 and 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their FrobeniusSchur indicators, their categorical Morita equivalence classes are distinguished by the set of the indicators and ribbon twists of their Drinfeld centers. In part...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2022
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2022.02.020