Related papers: The centre of the extended Haagerup subfactor has …

Linking systems are crucial for studying the homotopy theory of fusion systems, but are also of interest from an algebraic point of view. We propose a definition of a linking system associated to a saturated fusion system which is more…

The goal of this paper is to classify fusion categories $\otimes$-generated by a $K$-normal object (defined in this paper) of Frobenius-Perron dimension less than 2. This classification has recently become accessible due to a result of…

A group homomorphism $i: H \to G$ is a localization of $H$ if for every homomorphism $\varphi: H\rightarrow G$ there exists a unique endomorphism $\psi: G\rightarrow G$, such that $i \psi=\varphi$ (maps are acting on the right). G\"{o}bel…

Let $\Delta$ be a closed, cocompact subgroup of $G \times \widehat{G}$, where $G$ is a second countable, locally compact abelian group. Using localization of Hilbert $C^*$-modules, we show that the Heisenberg module…

We show the integrality of the simple Hurwitz numbers. The main tool is the cut-and-join operator, and our proof is a purely combinatorial one.

In a 2005 paper, Casacuberta, Scevenels and Smith construct a homotopy idempotent functor $E$ on the category of simplicial sets with the property that whether it can be expressed as localization with respect to a map $f$ is independent of…

We classify fusion categories which are Morita equivalent to even parts of subfactors with index $3+\sqrt{5} $, and module categories over these fusion categories. For the fusion category $\mathcal{C} $ which is the even part of the…

Locating the center of convex objects is important in both image processing and unsupervised machine learning/data clustering fields. The automated analysis of biological images uses both of these fields for locating cell nuclei and for…

We compare a heuristic count of components of the center variety in degree 3 with the equivalent count obtained from known families. From this comparison we conjecture that more than 100 unknown components exist.

We prove a conjecture due to Baumgaertel and Lledo according to which for every compact group G one has Z(G)^ \cong C(G), where the `chain group' C(G) is the free abelian group (written multiplicatively) generated by the set G^ of…

In this work, for a finite group $G$ and a 4-cocycle $\omega \in Z^4(G, \mathbf{k}^\times)$, we compute explicitly the center of the monoidal 2-category $\operatorname{2Vec}_G^{\omega}$ of $\omega$-twisted $G$-graded 1-categories of finite…

We construct a quasi-categorically enhanced Grothendieck six-functor formalism on schemes of finite type over the complex numbers. In addition to satisfying many of the same properties as M. Saito's derived categories of mixed Hodge…

We prove that the center of each degenerate cyclotomic Hecke algebra associated to the complex reflection group of type B_d(l) consists of symmetric polynomials in its commuting generators. The classification of the blocks of the degenerate…

We numerically study an anyon chain based on the Haagerup fusion category, and find evidence that it leads in the long-distance limit to a conformal field theory whose central charge is $\sim 2$. Fusion categories generalize the concept of…

Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…

We construct a family of infinite-dimensional positive sub-coalgebras within the Grothendieck ring of Hecke algebras, when viewed as a Hopf algebra with respect to the induction and restriction functor. These sub-coalgebras have as…

An equivalent definition of the Fibonacci numbers is that they are the unique sequence such that every integer can be written uniquely as a sum of non-adjacent terms. We can view this as we have bins of length 1, we can take at most one…

This paper uses Lusztig varieties to give central elements of the Iwahori-Hecke algebra corresponding to unipotent conjugacy classes in the finite Chevalley group $GL_n(\mathbb{F}_q)$. We explain how these central elements are related to…

We classify pointed fusion categories C(G, $\omega$) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2 3 , 2 4 and 3 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their…

Given a triangulated 2-Calabi-Yau category C and a cluster-tilting subcategory T, the index of an object X of C is a certain element of the Grothendieck group of the additive category T. In this note, we show that a rigid object of C is…