Pathlike co/bialgebras and their antipodes with applications to bi- and Hopf algebras appearing in topology, number theory and physics

DOI10.3842/SIGMA.2022.053zbMath1497.18031arXiv2104.08895OpenAlexW3153804882MaRDI QIDQ2162652

Ralph M. Kaufmann, Yang Mo

Publication date: 8 August 2022

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.08895

zbMATH Keywords

antipodescharactersgraphsHopf algebratreesbialgebrarenomalizationFeynman categorycolored structurescombinatorial coalgebraRota-Baxter

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Hopf algebras and their applications (16T05) Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads (18M85)

Related Items

Categorical models for path spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher Weil-Petersson volumes of moduli spaces of stable \(n\)-pointed curves
• The Hopf algebras of decorated rooted trees. II
• The QCD \(\beta \)-function from global solutions to Dyson-Schwinger equations
• On spineless cacti, Deligne's conjecture and Connes-Kreimer's Hopf algebra
• Antipodes and incidence coalgebras
• On the Hopf algebraic structure of Lie group integrators.
• The twisted Drinfeld double of a finite group via gerbes and finite groupoids
• The beginnings of the theory of Hopf algebras.
• Hopf algebras, renormalization and noncommutative geometry
• Braided tensor categories
• Lectures on Feynman categories
• Permutohedral structures on \(E_2\)-operads
• Feynman amplitudes, coaction principle, and cosmic Galois group
• Integrable renormalization. II: The general case
• On antipodes in pointed Hopf algebras
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Cochain level May-Steenrod operations
• Three Hopf algebras from number theory, physics \& topology, and their common background. I: Operadic \& simplicial aspects
• Three Hopf algebras from number theory, physics \& topology, and their common background. II: General categorical formulation
• Galois symmetries of fundamental groupoids and noncommutative geometry
• Homotopical algebra
• Free Hopf algebras generated by coalgebras
• Iterated integrals of differential forms and loop space homology
• Some aspects of Baxter's functional equation
• Rota-Baxter algebras, singular hypersurfaces, and renormalization on Kausz compactifications
• THE DRINFEL'D DOUBLE AND TWISTING IN STRINGY ORBIFOLD THEORY
• Coalgebras and Bialgebras in Combinatorics
• Hopf algebras and combinatorics
• Crossed Simplicial Groups and their Associated Homology
• Orbifolding Frobenius Algebras
• A duality theorem for hope module algebras over dedekind rings
• Outer Space as a Combinatorial Backbone for Cutkosky Rules and Coactions
• Feynman categories and representation theory
• Feynman Categories
• An Algebraic Theory of Integration Methods
• The Hopf algebra approach to Feynman diagram calculations
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• Quasi Hopf algebras, group cohomology and orbifold models
• Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group.
• A combinatorial Hopf algebra for nonlinear output feedback control systems
• Algebraic interplay between renormalization and monodromy