Related papers: Hopf Algebroids
We present several related examples of Hopf algebroids over a universal enveloping algebra which are of the scalar extension Hopf algebroid type and explain their origin in Lie and algebraic group theory.
We study the dual algebras of (discrete) Hopf algebroids. In particular, we understand comodules over a Hopf algebroid as (discrete) modules over its dual algebra.
We give some examples of, and raise some questions on, extensions of semisimple Hopf algebras.
Using methods from math-ph/9907010, we study families of Hopf algebra structures on coloured trees.
Some lower bounds of GK-dimension of Hopf algebras are given.
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…
Hopf algebroids are generalization of Hopf algebras over non-commutative base rings. It consists of a left- and a right-bialgebroid structure related by a map called the antipode. However, if the base ring of a Hopf algebroid is commutative…
We describe a topological ribbon Hopf algebra whose elements are sequences of matrices. The algebra is a quantum version of U(sl_2).
We provide an expository account of some of the Hopf algebras that can be defined using trees, labeled trees, ordered trees and heap ordered trees. We also describe some actions of these Hopf algebras on algebra of functions.
In late October 2004 I did a search on Hopf algebras in the database ZMATH to find out where they occur and what use is made of them (I.e. what applications there are). The result is a little astonishing, as can be seen from what follows.
We study certain subgroups of the full group of Hopf algebra automorphisms of a biproduct. In the process interesting subgroups of certain permutation groups come into play.
Two important generalizations of the Hopf algebra of symmetric functions are the Hopf algebra of noncommutative symmetric functions and its graded dual the Hopf algebra of quasisymmetric functions. A common generalization of the latter is…
The theory of integrals is used to analyse the structure of Hopf algebroids, introduced in math.QA/0302325. We prove that the total algebra of the Hopf algebroid is a separable extension of the base algebra if and only if it is a…
We survey Hopf algebras and their generalizations. In particular, we compare and contrast three well-studied generalizations (quasi-Hopf algebras, weak Hopf algebras, and Hopf algebroids), and two newer ones (Hopf monads and hopfish…
We define a "combinatorial Hopf algebra" as a Hopf algebra which is free (or cofree) and equipped with a given isomorphism to the free algebra over the indecomposables (resp. the cofree coalgebra over the primitives). The choice of such an…
We give examples of Lie-Rinehart algebras whose enveloping algebra is not a full Hopf algebroid in the sense of Bohm and Szlachanyi. We construct these examples as quotients of a canonical Lie-Rinehart algebra over a Jacobi algebra which…
This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics,…
We study the core Hopf algebra underlying the renormalization Hopf algebra.
The Hopf envelope of a bialgebra is the free Hopf algebra generated by the given bialgebra. Its existence, as well as that of the cofree Hopf algebra, is a well-known fact in Hopf algebra theory, but their construction is not particularly…
For arbitrary algebras $L$, we construct Hopf algebroids $A_\sigma$ with base rings $L$ by means of $\sigma^{ab}_{cd}\in L$ satisfying suitable properties.