منابع مشابه
On 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...
متن کاملThe periodic table of n-categories for low dimensions I: degenerate categories and degenerate bicategories
Abstract. We examine the periodic table of weak n-categories for the lowdimensional cases. It is widely understood that degenerate categories give rise to monoids, doubly degenerate bicategories to commutative monoids, and degenerate bicategories to monoidal categories; however, to understand this correspondence fully we examine the totalities of such structures together with maps between them ...
متن کاملOn 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...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2020
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2020.04.022