相关论文: Symmetries in Yetter-Drinfel'd-Long categories

Let $G$ be a finite group and let $\pi: G \to G'$ be a surjective group homomorphism. Consider the cocycle deformation $L = H^{\sigma}$ of the Hopf algebra $H = k^G$ of $k$-valued linear functions on $G$, with respect to some convolution…

Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…

Let $H$ be a Hopf algebra with bijective antipode over a field $k$ and suppose that $R{#}H$ is a bi-product. Then $R$ is a bialgebra in the Yetter--Drinfel'd category ${}_H^H{\mathcal YD}$. We describe the bialgebras $(R{#}H)^{op}$ and…

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 introduce Yetter-Drinfeld modules over a weak Hopf algebra $H$, and show that the category of Yetter-Drinfeld modules is isomorphic to the center of the category of $H$-modules. The categories of left-left, left-right, right-left and…

We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal bialgebra. We show that they correspond to modules and bimodules over the infinitesimal version of the double. We show that there is a natural,…

Let $H$ be a Hopf algebra and let $\mathcal D_H$ be a Hopf-module category. We describe the cocycles and coboundaries for the Hopf cyclic cohomology of $\mathcal D_H$, which correspond respectively to categorified cycles and vanishing…

We show homological mirror symmetry results relating coherent analytic sheaves on some complex elliptic surfaces and objects of certain Fukaya categories. We first define the notion of a non-algebraic Landau-Ginzburg model on $\mathbb{R}…

We continue the study of the representation theory of a regular weak multiplier bialgebra with full comultiplication, started in arXiv:1306.1466, arXiv:1311.2730. Yetter-Drinfeld modules are defined as modules and comodules, with…

Motivated by the work of of A. Zelevinsky on positive self-adjoint Hopf algebras, we define what we call a symmetric self-adjoint Hopf structure for a certain kind of semisimple abelian categories. It is known that every positive…

Let $H$ be a Hopf algebra. We consider $H$-equivariant modules over a Hopf module category $\mathcal C$ as modules over the smash extension $\mathcal C\# H$. We construct Grothendieck spectral sequences for the cohomologies as well as the…

Given a finite dimensional Hopf algebra H and an exact indecomposable module category M over Rep(H), we explicitly compute the adjoint algebra A_M as an object in the category of Yetter-Drinfeld modules over H, and the space of class…

Complex manifolds with compatible metric have a naturally defined subspace of harmonic differential forms that satisfy Serre, Hodge, and conjugation duality, as well as hard Lefschetz duality. This last property follows from a…

In this paper we explore new relations between Algebraic Topology and the theory of Hopf Algebras. For an arbitrary topological space $X$, the loop space homology $H_*(\Omega\Sigma X; \coefZ)$ is a Hopf algebra. We introduce a new homotopy…

We consider a q-analogue of the standard bilinear form on the commutative ring of symmetric functions. The q=-1 case leads to a Z-graded Hopf superalgebra which we call the algebra of odd symmetric functions. In the odd setting we describe…

For two families of Yetter-Drinfel'd Hopf algebras considered earlier by the authors, we determine which of them are isomorphic. We also determine which of their Radford biproducts are isomorphic.

Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories over the stable category of H-modules. These module-categories…

We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for…

We associate to each infinite primitive Lie pseudogroup a Hopf algebra of `transverse symmetries', by refining a procedure due to Connes and the first author in the case of the general pseudogroup. The affiliated Hopf algebra can be viewed…

We study Hopf algebras via tools from geometric invariant theory. We show that all the invariants we get can be constructed using the integrals of the Hopf algebra and its dual together with the multiplication and the comultiplication, and…