Feynman graphs, rooted trees, and Ringel-Hall algebras

DOI10.1007/s00220-008-0694-zzbMath1173.81008arXiv0806.1179OpenAlexW2009459090MaRDI QIDQ1028572

Kobi Kremnizer, Matthew Szczesny

Publication date: 6 July 2009

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.1179

zbMATH Keywords

Lie algebraFeynman graphRingel-Hall algebrarooted treecategorificationsymmetric monoidal category

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30)

Related Items (9)

On the Hall algebra of semigroup representations over \(\mathbb F_1\). ⋮ The Hopf algebra of skew shapes, torsion sheaves on \(\mathbb{A}_{/ \mathbb{F}_1}^n\), and ideals in Hall algebras of monoid representations ⋮ Incidence categories ⋮ Proto-exact categories of matroids, Hall algebras, and \(K\)-theory ⋮ Hall Lie algebras of toric monoid schemes ⋮ Degenerate versions of Green's theorem for Hall modules ⋮ Feynman graphs, rooted trees, and Ringel-Hall algebras ⋮ Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators ⋮ On left Hopf algebras within the framework of inhomogeneous quantum groups for particle algebras

Cites Work

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• Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Recursion and growth estimates in renormalizable quantum field theory
• Combinatorics of rooted trees and Hopf algebras

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