Related papers: Characterization of Hopf Quasigroups

We show basic results on super-manifolds and super Lie groups over a complete field of characteristic $\ne 2$, extensively using Hopf-algebraic techniques. The main results are two theorems. The first main theorem shows a category…

We show that if a finite dimensional Hopf algebra over ${\bf C}$ has a basis such that all the structure constants are non-negative, then the Hopf algebra must be given by a finite group $G$ and a factorization $G=G_+G_-$ into two…

In previous work, to each Hopf algebra H and each invertible right two-cocycle on H, Eli Aljadeff and the first-named author attached a subalgebra B of the free commutative Hopf algebra S generated by the coalgebra underlying H; the algebra…

Let G be an exceptional Lie group with a maximal torus T. Based on common properties in the Schubert presentation of the cohomology ring H*(G/T;F_{p}) DZ1, and concrete expressions of generalized Weyl invariants for G over F_{p}, we obtain…

In this paper we use the technique of Hopf algebras and quasi-symmetric functions to study the combinatorial polytopes. Consider the free abelian group $\mathcal{P}$ generated by all combinatorial polytopes. There are two natural bilinear…

The aim of this paper is to study quasitriangular structures on a class of semisimple Hopf algebras constructed through abelian extensions of $Z_2$ for an abelian group $G$. We prove that there are only two forms of them. Using such…

In this article -that has also the intention to survey some known results in the theory of compact quantum groups using methods different from the standard and with a strong algebraic flavor- we consider compact o-coalgebras and Hopf…

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 study the de-equivariantization of a Hopf algebra by an affine group scheme and we apply Tannakian techniques in order to realize it as the tensor category of comodules over a coquasi-bialgebra. As an application we construct a family of…

In this paper, we study the Hopf-Galois structures on a finite Galois extension whose Galois group $G$ is an almost simple group in which the socle $A$ has prime index $p$. Each Hopf-Galois structure is associated to a group $N$ of the same…

We discuss isomorphism questions concerning the Hopf algebras that yield Hopf-Galois structures for a fixed separable field extension $L/K$. We study in detail the case where $L/K$ is Galois with dihedral group $D_p$, $p\ge 3$ prime and…

Let H be a finite-dimensional quasi-Hopf algebra. We show for each quotient quasibialgebra Q of H that Q is a quasi-Hopf algebra whose dimension divides the dimension of H.

We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf…

We introduce and study a class of Hopf algebras $H(G, \chi, \eta, b, c, \beta)$ which are two-step Ore extensions of a group algebra $\mathbb{K}[G]$. This construction unifies and generalizes some known families of Hopf algebras such as…

We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and…

This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps. We use these constructions to prove some…

Certain sufficient homological and ring-theoretical conditions are given for a Hopf algebra to have bijective antipode with applications to noetherian Hopf algebras regarding their homological behaviors.

The main goal of this paper is to investigate the structure of Hopf algebras with the property that either its Jacobson radical is a Hopf ideal or its coradical is a subalgebra. In order to do that we define the Hochschild cohomology of an…

For a matrix coalgebra $C$ over some field, we determine all small subcoalgebras of the free Hopf algebra on $C$, the free Hopf algebra with a bjective antipode on $C$, and the free Hopf algebra with antipode $S$ satisfying $S^{2d}={\rm…

Let H be a quasi-Hopf algebra, a weak Hopf algebra or a braided Hopf algebra. Let B be an H-bicomodule algebra such that there exists a morphism of H-bicomodule algebras v:H\rightarrow B. Then we can define an object B^{co(H)} which is a…