Word Hopf algebras
Combinatorics
2007-05-23 v1 Quantum Algebra
Abstract
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 selfdual Hopf algebra of permutations (MPR Hopf algebra). This latter Hopf algebra can be seen as a Hopf algebra of endomorphisms of a Hopf algebra. That turns out to be a fruitful way of looking at things and gives rise to wide ranging further generalizations such as the word Hopf algebra and the double word Hopf algebra (and many more).
Cite
@article{arxiv.math/0410471,
title = {Word Hopf algebras},
author = {Michiel Hazewinkel},
journal= {arXiv preprint arXiv:math/0410471},
year = {2007}
}
Comments
This is an introductory and partial version for non Hopf algebra specialists of "Hopf algebras of endomorphisms of Hopf algebras (math.QA/0410364). 20 pages