Related papers: Decomposing Frobenius Heisenberg categories

We present a unified ring theoretic approach, based on properties of the Casimir element of a symmetric algebra, to a variety of known divisibility results for the degrees of irreducible representations of semisimple Hopf algebras in…

Cluster algebras *with coefficients* are important since they appear in nature as coordinate algebras of varieties like Grassmannians, double Bruhat cells, unipotent cells, ... . The approach of Geiss-Leclerc-Schr\"oer often yields…

We generalize the Frobenius-Schur theorem to $C^*$-categories. From this category-theoretical point of view, we introduce the notions of real, complex and quaternionic representations of Hopf $C^*$-algebras. Based on these definitions, we…

We discuss relations between some category-theoretical notions for a finite tensor category and cointegrals on a quasi-Hopf algebra. Specifically, for a finite-dimensional quasi-Hopf algebra $H$, we give an explicit description of…

We introduce continuous Frobenius categories. These are topological categories which are constructed using representations of the circle over a discrete valuation ring. We show that they are Krull-Schmidt with one indecomposable object for…

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 introduce a natural generalization of the definition of a symmetric Hopf algebroid, internal to any symmetric monoidal category with coequalizers that commute with the monoidal product. Motivation for this is the study of Heisenberg…

The degenerate Heisenberg category $\mathcal{H}eis_k$ is a strict monoidal category which was originally introduced in the special case $k=-1$ by Khovanov in 2010. Khovanov conjectured that the Grothendieck ring of the additive Karoubi…

We construct a Frobenius algebra structure on the Hochschild cochains of a group ring k[G] that extends the known structure of a <1, 2> topological quantum field theory on HH^0(k[G]; k[G]), k a field and G a finite group. The convolution…

We consider certain categorical structures that are implicit in subfactor theory. Making the connection between subfactor theory (at finite index) and category theory explicit sheds light on both subjects. Furthermore, it allows various…

Let $C$ be a nonsingular projective curve over an algebraically closed field of characteristic $p>0$ and $I\subset C$ be a finite set. If $\mathcal{U}_{C,\,\omega}$ denotes the moduli space of semistable parabolic bundles of rank $r$ and…

Let $f$ be an invertible polynomial and $G$ a group of diagonal symmetries of $f$. This note shows that the orbifold Jacobian algebra $\mathrm{Jac}(f,G)$ of $(f,G)$ defined by the authors and Elisabeth Werner in arXiv:1608.08962 is…

Jacobi/Poisson algebras are algebraic counterparts of Jacobi/Poisson manifolds. We introduce representations of a Jacobi algebra $A$ and Frobenius Jacobi algebras as symmetric objects in the category. A characterization theorem for…

We prove that for $X$ a quasi-compact $\mathbb{F}_p$-scheme with affine diagonal (e.g.\ $X$ quasi-compact and separated) there is a t-exact equivalence $\mathcal D(\mathrm{Frob}(\mathrm{QCoh}(X),F_*)) \to \mathrm{Frob}(\mathcal…

Suppose given a Frobenius category E, i.e. an exact category with a big enough subcategory B of bijectives. Let_E_ := E/B denote its classical stable category. For example, we may take E to be the category of complexes C(A) with entries in…

Frobenius-Schur indicators (or indicators for short) of objects in pivotal monoidal categories were defined and formulated by Ng and Schauenburg in 2007. In this paper, we introduce and study an analogous formula for indicators in the dual…

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 briefly report on our result that the braided tensor product algebra of two module algebras $A_1,A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $H_1$ with a subalgebra isomorphic to $A_2$…

We introduce and provide a classification theorem for the class of Heisenberg-Fock Leibniz algebras. This category of algebras is formed by those Leibniz algebras $L$ whose corresponding Lie algebras are Heisenberg algebras $H_n$ and whose…

Kaplansky conjectured that if H is a finite-dimensional semisimple Hopf algebra over an algebraically closed field k of characteristic 0, then H is of Frobenius type (i.e. if V is an irreducible representation of H then dimV divides dimH).…