On Hopf algebra structures over operads

Details On Hopf algebra structures over operads On Hopf algebra structures over operads

2004-07-06

arxiv.org/abs/math/0407074v2

Mathematics

Rings and Algebras

110 pages,with several minor corrections (references not updated)

Scientific paper

We study P-Hopf algebras with one coassociative cooperation over different operads P. For example, we consider the Loday-Ronco dendriform Hopf algebra and its isomorphisms with the noncommutative planar Connes-Kreimer Hopf algebra and with a Hopf algebra of Brouder and Frabetti. We focus on Hopf algebra structures over free operads, like the operad Mag freely generated by a non-commutative non-associative binary operation, and the operad of Stasheff polytopes. In order to describe the operads of primitive elements we prove an analogon of the Poincare-Birkhoff-Witt theorem. We determine the generating series for these operads and show that the dimension of PrimMag(n) is related to the log-Catalan numbers. By a recursive method we show how, for small n, these spaces can be described as modules over the symmetric groups.

Affiliated with

Also associated with

No associations

Rating

On Hopf algebra structures over operads 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 On Hopf algebra structures over operads, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Hopf algebra structures over operads will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-139742