相关论文: Cosovereign Hopf algebras

Given a Hopf algebra $A$ graded by a discrete group together with an action of the same group preserving the grading, we define a new Hopf algebra, which we call the graded twisting of $A$. If the action is adjoint, this new Hopf algebra is…

We introduce the Hopf algebra of uniform block permutations and show that it is self-dual, free, and cofree. These results are closely related to the fact that uniform block permutations form a factorizable inverse monoid. This Hopf algebra…

To every Hopf heap or quantum cotorsor of Grunspan a Hopf algebra of translations is associated. This translation Hopf algebra acts on the Hopf heap making it a Hopf-Galois co-object. Conversely, any Hopf-Galois co-object has the natural…

Let A be a finite dimensional unital associative algebra over a field K, which is also equipped with a coassociative counital coalgebra structure (\Delta,\eps). A is called a Weak Bialgebra if the coproduct \Delta is multiplicative. We do…

Let $ Aut_{mHH}(H)$ denote the set of all automorphisms of a monoidal Hopf algebra $H$ with bijective antipode in the sense of Caenepeel and Goyvaerts \cite{CG2011}. The main aim of this paper is to provide new examples of braided…

A new class of coefficients for the Hopf-cyclic homology of module algebras and coalgebras is introduced. These coefficients, termed stable anti-Yetter-Drinfeld contramodules, are both modules and contramodules of a Hopf algebra that…

Multiplier Hopf algebroids are algebraic versions of quantum groupoids that generalize Hopf algebroids to the non-unital case and weak (multiplier) Hopf algebras to non-separable base algebras. The main structure maps of a multiplier Hopf…

In this paper we outline an approach to calculus over quasitriangular Hopf algebras. We study differential operators in the framework of monoidal categories equipped with a braiding or symmetry. To be more concrete, we choose as an example…

Let H be a connected Hopf k-algebra of finite Gel'fand-Kirillov dimension over an algebraically closed field k of characteristic 0. The objects of study in this paper are the left or right coideal subalgebras T of H. They are shown to be…

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…

We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions over a dihedral group D_m, with m=4a> 11. We obtain this…

We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and in the theory of species. We prove that the composition of two cofree coalgebras is again cofree, and we give sufficient…

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…

Let $H$ be a Hopf algebra in a braided rigid monoidal category $\mathcal{V}$ admitting a coend $C$. We define a ``coend element'' of $H$ to be a morphism from $C$ to $H$. We then study certain coend elements of $H$, which generalize…

This notes gives a proof that a connected coaugmented cofiltered coalgebra is a conilpotent coalgebra and thus a connected coaugmented cofiltered bialgebra is a Hopf algebra. This applies in particular to a connected coaugmented cograded…

We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affine extension and prove soundness and completeness for the…

We define the fundamental group of a Hopf algebra over a field. For this purpose we first consider gradings of Hopf algebras and Galois coverings. The latter are given by linear categories with new additional structure which we call Hopf…

We suggest a generalization of Pontryagin duality from the category of commutative Stein groups to the category of (not necessarily commutative) Stein groups with algebraic connected component of identity. In contrast to the other similar…

We discuss some axioms that ensure that a Hopf algebra has its simple comodules classified using an analogue of the Borel-Weil construction. More precisely we show that a Hopf algebra having a dense big cell satisfies the above requirement.…

We classify exact indecomposable module categories over the representation category of all non-trivial Hopf algebras with coradical S_3 and S_4. As a byproduct, we compute all its Hopf-Galois extensions and we show that these Hopf algebras…