String-net models for nonspherical pivotal fusion categories
نویسندگان
چکیده
منابع مشابه
Higher Frobenius-schur Indicators for Pivotal Categories
We define higher Frobenius-Schur indicators for objects in linear pivotal monoidal categories. We prove that they are category invariants, and take values in the cyclotomic integers. We also define a family of natural endomorphisms of the identity endofunctor on a k-linear semisimple rigid monoidal category, which we call the Frobenius-Schur endomorphisms. For a k-linear semisimple pivotal mono...
متن کاملCoherence of Proof-Net Categories
The notion of proof-net category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly’s and Mac Lane’s coherence theorem for symmetric monoidal closed categories. A coherence theorem with respect to these graphs is proved for proof-net categories. Such a coherence ...
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 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 Knot Theory and Its Ramifications
سال: 2020
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216520500352