Related papers: Module traces and Hopf group-coalgebras
In this paper we study the properties of Drinfeld's twisting for finite-dimensional Hopf algebras. We determine how the integral of the dual to a unimodular Hopf algebra $H$ changes under twisting of $H$. We show that the classes of…
We formulate the generation of finite dimensional pointed Hopf algebras by group-like elements and skew-primitives in geometric terms. This is done through a more general study of connected and coconnected Hopf algebras inside a braided…
Let H be a finite-dimensional Hopf algebra. We give a description of the tensor product of bimodule categories over Rep(H). When the bimodule categories are invertible this description can be given explicitly. We present some consequences…
We study the structure of the category of graded, connected, countable-dimensional, commutative and cocommutative Hopf algebras over a perfect field $k$ of characteristic $p$. Every $p$-torsion object in this category is uniquely a direct…
We initiate a study of tensor ideals in linear rigid monoidal categories that are kernels of linear monoidal functors to abelian monoidal categories. We develop general methods and apply them to the category of tilting modules over quantum…
We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We…
Our first collection of results parametrize (filtered) actions of a quantum Borel $U_q(\mathfrak{b}) \subset U_q(\mathfrak{sl}_2)$ on the path algebra of an arbitrary (finite) quiver. When $q$ is a root of unity, we give necessary and…
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…
We introduce the notions of categorical integrals and categorical cointegrals of a finite tensor category $\mathcal{C}$ by using a certain adjunction between $\mathcal{C}$ and its Drinfeld center $\mathcal{Z}(\mathcal{C})$. These notions…
We study the algebra of conformal endomorphisms $\Cend^{G,G}_n$ of a finitely generated free module $M_n$ over the coordinate Hopf algebra $H$ of a linear algebraic group $G$. It is shown that a conformal subalgebra of $\Cend_n$ acting…
We define notions of pivotal and ribbon objects in a monoidal category. These constructions give pivotal or ribbon monoidal categories from a monoidal category which is not necessarily with duals. We apply this construction to the braided…
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…
In this paper we introduce the notion of generalized invertible 1-cocycle in a strict braided monoidal category C, and we prove that the category of Hopf trusses is equivalent to the category of generalized invertible 1-cocycles. On the…
The aim of this note is to understand under which conditions invertible modules over a commutative S-algebra in the sense of Elmendorf, Kriz, Mandell and May give rise to elements in the algebraic Picard group of invertible graded modules…
Generalising a result for Hopf algebras, we not only define the four possible types of Hopf modules in the bialgebroid setting but also yield the notion of two-sided two-cosided Hopf modules, also known as Hopf bimodules or tetramodules, in…
Let C be a finite EI category and k be a field. We consider the category algebra kC. Suppose K(C)=D^b(kC-mod) is the bounded derived category of finitely generated left modules. This is a tensor triangulated category and we compute its…
We show that the functor of $p$-typical co-Witt vectors on commutative algebras over a perfect field $k$ of characteristic $p$ is defined on, and in fact only depends on, a weaker structure than that of a $k$-algebra. We call this structure…
In this work, the notion of partial representation of a Hopf algebra is introduced and its relationship with partial actions of Hopf algebras is explored. Given a Hopf algebra $H$, one can associate it to a Hopf algebroid $H_{par}$ which…
Motivated by the study of von Neumann regular skew groups as carried out by Alfaro, Ara and del Rio in 1995 we investigate regular and biregular Hopf module algebras. If $A$ is an algebra with an action by an affine Hopf algebra $H$, then…
For a complex connected reductive group G, we classify the simple modules whose cone of primitive vectors admits a nontrivial G-invariant deformation. We relate this classification to that of simple Jordan algebras, and to that (due to…