The Malvenuto-Reutenauer Hopf Algebra of Permutations

Table of Contents

  1. Monomial Functions in terms of the Fundamental Basis.
  2. Products in the Fundamental Basis.
  3. Products in the Monomial Basis.
  4. Antipode in the Fundamental Basis.
  5. Antipode in the Monomial Basis.
  6. Lie Bracket of Primitive Elements.
  7. Hopf cocycle on primitive elements for smash product of decomposiiton of SSym.
  8. Hopf cocycle on elements of the M-basis of QSym.
Bibliography
[AS02] M. Aguiar and F. Sottile, Structure of the Malvenuto-Reutenauer Hopf algebra of permutations, with Marcelo Aguiar, Advances in Mathematics 191, (2005), 225--275.
[AS06]                   , Structure of the Loday-Ronco Hopf algebra of trees, with Marcelo Aguiar, Journal of Algebra, Volume 295, Issue 2 , 15 January 2006, Pages 473-511.
Last Modified: 4 August 2002 by Frank Sottile