Bidendriform bialgebras, trees, and free quasi-symmetric functions

Details Bidendriform bialgebras, trees, and free quasi-symmetric functions Bidendriform bialgebras, trees, and free quasi-symmetric functions

2005-05-11

arxiv.org/abs/math/0505207v1

Mathematics

Rings and Algebras

33 pages

Scientific paper

We introduce bidendriform bialgebras, which are bialgebras such that both product and coproduct can be split into two parts satisfying good compatibilities. For example, the Malvenuto-Reutenauer Hopf algebra and the non-commutative Connes-Kreimer Hopf algebras of planar decorated rooted trees are bidendriform bialgebras. We prove that all connected bidendriform bialgebras are generated by their primitive elements as a dendriform algebra bidendriform Milnor-Moore theorem) and then is isomorphic to a Connes-Kreimer Hopf algebra. As a corollary, the Hopf algebra of Malvenuto-Reutenauer is isomorphic to the Connes-kreimer Hopf algebra of planar rooted trees decorated by a certain set. We deduce that the Lie algebra of its primitive elements is free in characteristic zero (G. Duchamp, F. Hivert and J.-Y. Thibon conjecture).

Affiliated with

Also associated with

No associations

Rating

Bidendriform bialgebras, trees, and free quasi-symmetric functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bidendriform bialgebras, trees, and free quasi-symmetric functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bidendriform bialgebras, trees, and free quasi-symmetric functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-73528