Les algebres de Hopf des arbres enracines decores
| dc.creator | Foissy, Loic | |
| dc.date | 2001-05-25 | |
| dc.date.accessioned | 2026-07-07T04:41:51Z | |
| dc.date.available | 2026-07-07T04:41:51Z | |
| dc.description | In \cite{Kreimer1,Connes,Broadhurst,Kreimer2}, a commutative, non cocommutative Hopf algebra H_R of (decorated) rooted trees was introduced. It is related to the Hopf algebra H_CM introduced in \cite{Moscovici}. Its dual Hopf algebra is the enveloping algebra of the Lie algebra of rooted trees L^1. In this paper, we introduce a non commutative, non cocommutative Hopf algebra H_PR of decorated planar rooted trees. We first show that H_PR is self dual. We then use this result to construct a non degenerate bilinear form (,) on H_PR, which respects the Hopf algebra structure of H_PR. Moreover, we give a combinatorial expression for the bilinear form (,). This allows us to give a direct formula for a basis of the primitive elements of H_PR. In the next sections, we show that H_PR is isomorphic to the Hopf algebra of planar binary trees introduced in \cite{Frabetti, Brouder}, and construct a subalgebra of formal non commutative diffeomorphisms. We then classify the Hopf algebra endomorphisms and coalgebra endomorphisms of H_PR. In the last sections, we give results about tensorial coalgebras and apply them to H_PR and H_R. We show how to construct the primitive elements of H_R from the primitive elements of H_PR and finally prove that L^1 is a free Lie algebra. | |
| dc.description | LaTeX, 73 pages (paper in French) | |
| dc.identifier | https://arxiv.org/abs/math/0105212 | |
| dc.identifier | http://arxiv.org/abs/math/0105212 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61534 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16W30 (Primary) 81T15, 05C05 (Secondary) | |
| dc.title | Les algebres de Hopf des arbres enracines decores | |
| dc.type | text |