Structure of The Malvenuto-Reutenauer Hopf Algebra of Permutations (Extended Abstract)

Authors

Marcelo Aguiar
Frank Sottile

Publication Date

2002

Abstract

We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primitive elements and its coradical filtration and show that it decomposes as a crossed product over the Hopf algebra of quasi-symmetric functions. We also describe the structure constants of the multiplication as a certain number of facets of the permutahedron. Our results reveal a close relationship between the structure of this Hopf algebra and the weak order on the symmetric groups.

Comments

This paper was harvested from ArXiv.org and ArXiv identifier is arXiv:0203101v2

Recommended Citation

Aguiar, Marcelo and Sottile, Frank, "Structure of The Malvenuto-Reutenauer Hopf Algebra of Permutations (Extended Abstract)" (2002). Mathematics and Statistics Department Faculty Publication Series. 7.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/7