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...
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 کاملOn non-semisimple fusion rules and tensor categories
Category theoretic aspects of non-rational conformal field theories are discussed. We consider the case that the category C of chiral sectors is a finite tensor category, i.e. a rigid monoidal category whose class of objects has certain finiteness properties. Besides the simple objects, the indecomposable projective objects of C are of particular interest. The fusion rules of C can be block-dia...
متن کاملOn weakly group-theoretical non-degenerate braided fusion categories
We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. This applies in particular to solvable nondegenerate braided fusion categories. We also give some sufficient conditions for a braided fusion category to be weakly group-theo...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2005
ISSN: 0003-486X
DOI: 10.4007/annals.2005.162.581