相关论文: On fusion categories

S. Montgomery and S. Witherspoon proved that upper and lower semisolvable, semisimple, finite dimensional Hopf algebras are of Froebenius type when their dimensions are not divisible by the characteristic of the base field. In this note we…

In this paper, we extend a classical vanishing result of Burnside from the character tables of finite groups to the character tables of commutative fusion rings, or more generally to a certain class of abelian normalizable hypergroups. We…

We provide a parameterization of all fusion subcategories of the equivariantization by a group action on a fusion category. As applications, we classify the Hopf subalgebras of a family of semisimple Hopf algebras of Kac-Paljutkin type and…

We prove that any fusion category over $\mathbb{C}$ with exactly one non-invertible simple object is spherical. Furthermore, we classify all such categories that come equipped with a braiding.

We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension.…

We call a finitely complete category algebraically coherent when the change-of-base functors of its fibration of points are coherent, which means that they preserve finite limits and jointly strongly epimorphic pairs of arrows. We give…

In this paper we give a new foundational, categorical formulation for operations and relations and objects parameterizing them. This generalizes and unifies the theory of operads and all their cousins including but not limited to PROPs,…

Algebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the…

We define a symmetric tensor enhancement $\mathrm{E}\mathbb{F}$ with full duals of the 3-category $\mathbb{F}$ of fusion categories in which every Reshetikhin--Turaev theory has a fully local realization. Our $\mathrm{E}\mathbb{F}$ is a…

Coecke and Heunen described completely positive maps in dagger monoidal categories and the {\sf CP}-infinity construction on these categories in order to construct a category of arbitrary dimensional quantum processes. This article…

For a large class of geometric objects, the passage to categories of quasi-coherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a…

Under certain conditions, a scheme can be reconstructed from its category of quasi-coherent sheaves. The Tannakian reconstruction theorem provides another example where a geometric object can be reconstructed from an associated category, in…

We develop the theory of semisimple weak Hopf algebras and obtain analogues of a number of classical results for ordinary semisimple Hopf algebras. We prove a criterion for semisimplicity and analyze the square of the antipode S^2 of a…

We use factorizable finite tensor categories, and specifically the representation categories of factorizable ribbon Hopf algebras H, as a laboratory for exploring bulk correlation functions in local logarithmic conformal field theories. For…

We develop a theory of curved A-infinity-categories around equivalences of their module categories. This allows for a uniform treatment of curved and uncurved A-infinity-categories which generalizes the classical theory of uncurved…

This thesis contains results relevant for two different classes of conformal field theory. We partly treat rational conformal field theory, but also derive results that aim at a better understanding of logarithmic conformal field theory.…

We prove that, in case $A(c)$ = the FRT construction of a braided vector space $(V,c)$ admits a weakly Frobenius algebra $\mathfrak B$ (e.g. if the braiding is rigid and its Nichols algebra is finite dimensional), then the Hopf envelope of…

Let C be a fusion category which is an extension of a fusion category D by a finite group G. We classify module categories over C in terms of module categories over D and the extension data (c,M,a) of C. We also describe functor categories…

For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal…

Grothendieck-Verdier duality is a powerful and ubiquitous structure on monoidal categories, which generalises the notion of rigidity. Hopf algebroids are a generalisation of Hopf algebras, to a non-commutative base ring. Just as the…