Non-commutative Hopf algebra of formal diffeomorphisms.
From MaRDI portal
Publication:818051
DOI10.1016/j.aim.2005.01.005zbMath1133.16025arXivmath/0406117OpenAlexW1964720703MaRDI QIDQ818051
Christian Krattenthaler, Alessandra Frabetti, Christian Brouder
Publication date: 24 March 2006
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0406117
convolution productscoproductsHopf algebrasantipodescoalgebrasLaurent seriesgenerating seriesgroups of formal power seriesformal diffeomorphisms
Related Items
Lie groups of controlled characters of combinatorial Hopf algebras ⋮ A renormalized rough path over fractional Brownian motion ⋮ Combinatorial Hopf algebras from PROs ⋮ Noncommutative symmetric functions and Lagrange inversion. II: Noncrossing partitions and the Farahat-Higman algebra ⋮ Noncommutative Bell polynomials, quasideterminants and incidence Hopf algebras ⋮ Renormalization as a functor on bialgebras ⋮ Combinatorial properties of the noncommutative Faà di Bruno algebra. ⋮ A simplicial groupoid for plethysm ⋮ Combinatorial Hopf algebras from renormalization ⋮ Inverse relations and reciprocity laws involving partial Bell polynomials and related extensions ⋮ A Faà di Bruno subalgebra of the graded dual of word symmetric functions ⋮ On the algebra of quasi-shuffles. ⋮ An antipode formula for the natural Hopf algebra of a set operad. ⋮ Nilpotent Sabinin algebras ⋮ Exponential renormalization ⋮ Plethysms and operads ⋮ Quotient Hopf algebras of the free bialgebra with PBW bases and GK-dimensions ⋮ Combinatorics of Poincaré’s and Schröder’s equations ⋮ Polynomial functors and combinatorial Dyson–Schwinger equations ⋮ Polynomial realizations of some combinatorial Hopf algebras ⋮ A unified approach to generating series for mixed cascades of analytic nonlinear input–output systems ⋮ Lagrange inversion ⋮ Noncommutative free cumulants ⋮ Groups of tree-expanded series. ⋮ Noncommutative symmetric functions and Lagrange inversion ⋮ The loop of formal power series with noncommutative coefficients under substitution ⋮ Loop of formal diffeomorphisms and Faà di Bruno coloop bialgebra ⋮ A Faà di Bruno Hopf algebra for a group of fliess operators with applications to feedback ⋮ A rough path over multidimensional fractional Brownian motion with arbitrary Hurst index by Fourier normal ordering ⋮ Zimmermann type cancellation in the free Faà di Bruno algebra ⋮ The incidence comodule bialgebra of the Baez-Dolan construction ⋮ Hölder-continuous rough paths by Fourier normal ordering ⋮ Hopf Algebras in Renormalisation ⋮ Faà di Bruno for operads and internal algebras ⋮ Faà di Bruno's formula and inversion of power series ⋮ Quantum field theory meets Hopf algebra ⋮ The structure of renormalization Hopf algebras for gauge theories. I: Representing Feynman graphs on BV-algebras ⋮ Free cumulants, Schröder trees, and operads
Cites Work
- Poisson geometrical symmetries associated to non-commutative formal diffeomorphisms
- Die Lagrange-Bürmannsche Formel bei formalen Potenzreihen. (Lagrange-Bürmann formula for formal power series)
- A combinatorial proof of the multivariable Lagrange inversion formula
- Semi-direct products of Hopf algebras
- Hopf algebra of the planar binary trees
- Cogroups in algebras over an operad are free algebras
- Incidence Hopf algebras
- Comparison of Hopf algebras on trees.
- QED Hopf algebras on planar binary trees.
- Cofree Hopf algebras.
- Charges from dressed matter: construction
- Charges from dressed matter: Physics and renormalisation
- Eulerian idempotents and Milnor-Moore theorem for certain non-cocommutative Hopf algebras
- Arithmetree.
- Künneth-style formula for the homology of Leibniz algebras
- Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
- Groups of tree-expanded series.
- A Milnor–Moore theorem for dendriform Hopf algebras
- Free Random Variables
- On the structure of cofree Hopf algebras
- A Noncommutative Generalization and q-Analog of the Lagrange Inversion Formula
- Coalgebras and Bialgebras in Combinatorics
- Local covariant quantum field theory over spectral geometries
- Renormalization of QED with planar binary trees
- Dialgebras and related operads
- The Hopf algebra structure of Connes and Kreimer in Epstein-Glaser renormalization
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item