Fusion Categories Of
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چکیده
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.
منابع مشابه
On the classification of certain fusion categories
We advance the classification of fusion categories in two directions. Firstly, we completely classify integral fusion categories — and consequently, semisimple Hopf algebras — of dimension pq2, where p and q are distinct primes. This case is especially interesting because it is the simplest class of dimensions where not all integral fusion categories are group-theoretical. Secondly, we classify...
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We answer three closely related questions concerning the Haagerup subfactor and its even parts, the Haagerup fusion categories. Namely we find all simple module categories over each of the Haagerup fusion categories (in other words, we find the “quantum subgroups” in the sense of Ocneanu), we find all subfactors whose principal even part is one of the Haagerup fusion categories, and we compute ...
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We give an explicit description, up to gauge equivalence, of group-theoretical quasi-Hopf algebras. We use this description to compute the Frobenius-Schur indicators for grouptheoretical fusion categories.
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We give a necessary and sufficient condition in terms of group cohomology for two indecomposable module categories over a group-theoretical fusion category C to be equivalent. This concludes the classification of such module categories.
متن کاملNear-group fusion categories and their doubles
A near-group fusion category is a fusion category C where all but 1 simple objects are invertible. Examples of these include the Tambara-Yamagami categories and the even sectors of the D (1) 5 and E6 subfactors, though there are infinitely many others. We classify the near-group fusion categories, and compute their doubles and the modular data relevant to conformal field theory. Among other thi...
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تاریخ انتشار 2003