Cocommutative Hopf algebras of permutations and trees Academic Article

abstract

• Consider the coradical filtrations of the Hopf algebras of planar binary trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We give explicit isomorphisms showing that the associated graded Hopf algebras are dual to the cocommutative Hopf algebras introduced in the late 1980's by Grossman and Larson. These Hopf algebras are constructed from ordered trees and heap-ordered trees, respectively. These results follow from the fact that whenever one starts from a Hopf algebra that is a cofree graded coalgebra, the associated graded Hopf algebra is a shuffle Hopf algebra. 2005 Springer Science + Business Media, Inc.

authors

• Sottile, Frank

published proceedings

• JOURNAL OF ALGEBRAIC COMBINATORICS

author list (cited authors)

• Aguiar, M., & Sottile, F.

citation count

• 14

complete list of authors

• Aguiar, M||Sottile, F

publication date

• January 2005

publisher

• Springer Nature  Publisher

published in

• Journal of Algebraic Combinatorics: an international journal  Journal

keywords

• Hopf Algebra
• Planar Binary Tree
• Rooted Tree
• Symmetric Group

Digital Object Identifier (DOI)

• 10.1007/s10801-005-4628-y

start page

• 451

end page

• 470

volume

• 22

issue

• 4

URL

• http://dx.doi.org/10.1007/s10801-005-4628-y