Let k be a field and let S n be the symmetric group. The group algebra k[S n ] contains the Solomon descent algebra, which is of dimension 2 n&1 . In [MR] Malvenuto and Reutenauer construct a graded Hopf algebra structure on so that the sum of the Solomon descent algebras There is a basis In betw
β¦ LIBER β¦
QED Hopf algebras on planar binary trees
β Scribed by Christian Brouder; Alessandra Frabetti
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 190 KB
- Volume
- 267
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper we describe the Hopf algebras on planar binary trees used to renormalize the Feynman propagators of quantum electrodynamics, and the coaction which describes the renormalization procedure. Both structures are related to some semi-direct coproduct of Hopf algebras.
π SIMILAR VOLUMES
Hopf Algebra of the Planar Binary Trees
β
Jean-Louis Loday; MarΔ±́a O. Ronco
π
Article
π
1998
π
Elsevier Science
π
English
β 416 KB