相关论文: Pseudo-unitary non-self-dual fusion categories of …

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 E6 and affine-D5 subfactors, though there are…

In this text, we study derived versions of the fusion category associated to Lusztig's quantum group $\textbf{U}_q$. The categories that so arise are non-semisimple but recovers the usual fusion ring when passing to complexified…

We give two proofs of a level-rank duality for braided fusion categories obtained from quantum groups of type $C$ at roots of unity. The first proof uses conformal embeddings, while the second uses a classification of braided fusion…

In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion category C, and then introduce the upper central…

We classify (multi)fusion 2-categories in terms of braided fusion categories and group cohomological data. This classification is homotopy coherent -- we provide an equivalence between the 3-groupoid of (multi)fusion 2-categories up to…

Let $R$ be a right notherian ring. We introduce the concept of relative singularity category $\Delta_{\mathcal{X}}(R)$ of $R$ with respect to a contravariantly finite subcategory $\mathcal{X}$ of $\rm{mod}\mbox{-}R.$ Along with some…

In this paper, we define a Grothendieck ring as a fusion ring categorifiable into a fusion category over the complex field. An integral fusion ring is called Drinfeld if all its formal codegrees are integers dividing the global…

A finite tensor category is called pointed if all its simple objects are invertible. We find necessary and sufficient conditions for two pointed semisimple categories to be dual to each other with respect to a module category. Whenever the…

We introduce fusion bialgebras and their duals and systematically study their Fourier analysis. As an application, we discover new efficient analytic obstructions on the unitary categorification of fusion rings. We prove the Hausdorff-Young…

Bimonoidal categories are categorical analogues of rings without additive inverses. They have been actively studied in category theory, homotopy theory, and algebraic $K$-theory since around 1970. There is an abundance of new applications…

In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for $so(2p+1)_2$. These categories describe non-abelian anyons dubbed `metaplectic anyons'. We…

We study generalizations of the non-invertible duality defects present in $\mathcal{N} = 4$ SU(N) SYM by studying theories with larger duality groups. We focus on 4d $\mathcal{N} = 2$ theories of class $\mathcal{S}$ obtained by the…

We classify modular fusion categories up to braided equivalence with less than four distinct twists of simple objects by observing that under this assumption, for each positive integer $N$, there are finitely many modular fusion categories…

We classify braided generalized near-group fusion categories whose global dimension is not an integer; there are exactly two up to Grothendieck equivalence and taking products with braided pointed fusion categories.

Let C be the category of finite-dimensional representations of a quantum affine algebra of simply-laced type. We introduce certain monoidal subcategories C_l (l integer) of C and we study their Grothendieck rings using cluster algebras.

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.

A semidualizing module is a generalization of Grothendieck's dualizing module. For a local Cohen-Macaulay ring $R$, the ring itself and its canonical module are always realized as (trivial) semidualizing modules. Reasonably, one might…

Recall that the definition of the $K$-theory of an object C (e.g., a ring or a space) has the following pattern. One first associates to the object C a category A_C that has a suitable structure (exact, Waldhausen, symmetric monoidal, ...).…

The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an…

We prove a rank-finiteness conjecture for modular categories: up to equivalence, there are only finitely many modular categories of any fixed rank. Our technical advance is a generalization of the Cauchy theorem in group theory to the…