Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations.

DOI10.1016/j.aim.2007.12.003zbMath1158.16020arXiv0707.1204OpenAlexW2594760764MaRDI QIDQ2482055

Loïc Foissy

Publication date: 16 April 2008

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1204

zbMATH Keywords

Faà di Bruno Hopf algebrasHopf algebras of rooted trees

Mathematics Subject Classification ID

Related Items (34)

A new perspective on intermediate algorithms via the Riemann-Hilbert correspondence ⋮ Combinatorial Hopf algebras from PROs ⋮ Graphons and renormalization of large Feynman diagrams ⋮ Resonant resurgent asymptotics from quantum field theory ⋮ Combinatorial properties of the noncommutative Faà di Bruno algebra. ⋮ Modules of the 0-Hecke algebra and quasisymmetric Schur functions ⋮ A one-parameter deformation of the Farahat-Higman algebra. ⋮ Two interacting coordinate Hopf algebras of affine groups of formal series on a category. ⋮ Sequences of trees and higher-order renormalization group equations ⋮ Log expansions from combinatorial Dyson-Schwinger equations ⋮ Locality and renormalization: Universal properties and integrals on trees ⋮ From Dyson-Schwinger equations to quantum entanglement ⋮ The combinatorics of a tree-like functional equation for connected chord diagrams ⋮ Lie algebras associated to systems of Dyson-Schwinger equations. ⋮ Backward error analysis and the substitution law for Lie group integrators ⋮ Polynomial functors and combinatorial Dyson–Schwinger equations ⋮ Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees. ⋮ General Dyson-Schwinger equations and systems ⋮ Multigraded Dyson–Schwinger systems ⋮ A unified approach to generating series for mixed cascades of analytic nonlinear input–output systems ⋮ FROM DYSON–SCHWINGER EQUATIONS TO THE RIEMANN–HILBERT CORRESPONDENCE ⋮ A Faà di Bruno Hopf algebra for a group of fliess operators with applications to feedback ⋮ Classification of systems of Dyson-Schwinger equations in the Hopf algebra of decorated rooted trees. ⋮ Hopf algebra structure of generalized quasi-symmetric functions in partially commutative variables ⋮ Generalized chord diagram expansions of Dyson-Schwinger equations ⋮ Faà di Bruno for operads and internal algebras ⋮ On two constructions of an effective field theory ⋮ Solution of the Differential Equation $y^{(k)}=e^{ay}$, Special Values of Bell Polynomials and $(k,a)$-Autonomous Coefficients ⋮ A ONE-PARAMETER DEFORMATION OF THE NONCOMMUTATIVE LAGRANGE INVERSION FORMULA ⋮ Renormalization and Mellin Transforms ⋮ The structure of renormalization Hopf algebras for gauge theories. I: Representing Feynman graphs on BV-algebras ⋮ A pre-Lie algebra associated to a linear endomorphism and related algebraic structures ⋮ MOTIVIC DYSON–SCHWINGER EQUATIONS ⋮ THE GLOBAL β-FUNCTIONS FROM SOLUTIONS OF DYSON–SCHWINGER EQUATIONS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Hopf algebras of decorated rooted trees. II
• Hopf algebras, renormalization and noncommutative geometry
• On the Hopf algebra strucutre of perturbative quantum field theories
• Hopf algebras, cyclic cohomology and the transverse index theorem
• Comparison of Hopf algebras on trees.
• Combinatorics of (perturbative) quantum field theory
• The Hopf algebras of decorated rooted trees. I
• Trees, renormalization and differential equations.
• On overlapping divergences
• Finite dimensional comodules over the Hopf algebra of rooted trees
• Duality between quasi-symmetric functions and the Solomon descent algebra
• Zimmermann type cancellation in the free Faà di Bruno algebra
• On the structure of Hopf algebras
• Combinatorics of rooted trees and Hopf algebras
• Towards cohomology of renormalization: bigrading the combinatorial Hopf algebra of rooted trees

This page was built for publication: Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations.