Related papers: Linkable Dynkin Diagrams

In this paper we construct and study two new families of finite dimensional pointed Hopf algebras which generalize Radford's families. We show that over any infinite field which contains a primitive nth root of unity, one of the families…

Let p be a prime, and k be a field of characteristic p. We investigate the algebra structure and the structure of the cohomology ring for the connected Hopf algebras of dimension p^3, which appear in the classification obtained in [V.C.…

We define and study a combinatorial Hopf algebra dRec with basis elements indexed by diagonal rectangulations of a square. This Hopf algebra provides an intrinsic combinatorial realization of the Hopf algebra tBax of twisted Baxter…

Let $\mathbb{k}$ be an algebraically closed field of characteristic zero. Let $D$ be a division algebra of degree $d$ over its center $Z(D)$. Assume that $\mathbb{k}\subset Z(D)$. We show that a finite group $G$ faithfully grades $D$ if and…

Action of finite-dimensional Hopf algebra $H$ on commutative $k-$algebra $A$ is considered. As a generalization of the well-known fact for finite groups S. Montgomery raised a problem in 1993 whether $A$ is integral over subalgebra of…

S. Montgomery and S. Witherspoon proved that upper and lower semisolvable, semisimple, finite dimensional Hopf algebras are of Froebenius type when their dimensions are not divisible by the characteristic of the base field. In this note we…

The usual vertex algebras have as underlying symmetry the Hopf algebra $H_D=\mathbb C[D]$ of infinitesimal translations. We show that it is possible to replace $H_D$ by another symmetry algebra $H_T=\mathbb C[T,T\inv]$, the group algebra of…

It is known that the vector space spanned by labeled rooted trees forms a Hopf algebra. Let k be a field and let R be a commutative k-algebra. Let H denote the Hopf algebra of rooted trees labeled using derivations D in Der(R). In this…

This is the fifth article in the Derived Langlands series which consists of one monograph and four articles. In this article I describe the Hopf algebra and Positive Selfadjoint Hopfalgebra (PSH) aspects to classification of a number of new…

In this paper we describe the right-sided combinatorial Hopf structure of three Hopf algebras appearing in the context of renormalization in quantum field theory: the non-commutative version of the Fa\`a di Bruno Hopf algebra, the…

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in…

Let H be a cosemisimple Hopf algebra over an algebraically closed field k which contains a simple subcoalgebra of dimension 9. We show that if H has no simple subcoalgebras of even dimension then H contains either a grouplike element with…

Anti-cocommutativity was introduced by Wang, Zhuang, Zhang (2013) in their paper Coassociative Lie algebras. Since universal enveloping algebras of Lie algebras are connected Hopf algebras, we extend enveloping algebras using the notion of…

Hopf algebroids are generalizations of Hopf algebras to less commutative settings. We show how the comultiplication defined by Kostant and Kumar turns the affine nil Hecke algebra associated to a Coxeter system into a Hopf algebroid without…

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 study some aspects of the theory of non-commutative differential calculi over complex algebras, especially over the Hopf algebras associated to compact quantum groups in the sense of S.L. Woronowicz. Our principal emphasis is on the…

This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure…

Lie-Rinehart algebras, also known as Lie algebroids, give rise to Hopf algebroids by a universal enveloping algebra construction, much as the universal enveloping algebra of an ordinary Lie algebra gives a Hopf algebra, of infinite…

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…

In this paper, we provide the structure of Hopf graphs associated to pairs $(G, \mathfrak{r})$ consisting of groups $G$ together with ramification datas $\mathfrak{r}$ and their Leavitt path algebras. Consequently, we characterize the…