High Energy Physics - Theory · arXiv:0902.1223 v1 · submitted 7 Feb 2009
The core Hopf algebra
The paper says
“We study the core Hopf algebra underlying the renormalization Hopf algebra.”
from the abstract · picked out as the main claim by a classifier
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The paper
Abstract
We study the core Hopf algebra underlying the renormalization Hopf algebra.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 0.71
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.04 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.05 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We study the core Hopf algebra underlying the renormalization Hopf algebra. | contribution 1.00 | 0.88 | 0.14 | asserted 0.71 |
What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.95
What was examined, and what was not
Sources read
- arXiv listing abstract v1
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- full text
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- references and citing sentences
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- P abstract
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- S sections
- T body sentences
- C citations
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,556 input tokens, $0.0001 reported.
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Cited by 2 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- The algebraic structure of cut Feynman integrals and the diagrammatic coaction hep-th · Mar 2017
- Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case hep-th · Apr 2017
How the literature uses it
18 arXiv papers cite this in 26 sentences
Papers citing it · 16 sentences without a confident label
Builds on it 1 paper
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Here, we generalize such a setup to Cutkosky graphs and graphs with forests, starting from the core Hopf algebra [ref] .
Algebraic Interplay between Renormalization and Monodromy · Hopf algebras · 1.00
Compares with it 1 paper
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Slightly less general results in this direction can be found in [ref] , some of them using the language of Hochschild cohomology.[We also mention the relevant conference proceedings [ref] .]
Gauge Symmetries and Renormalization · Quantum gauge symmetries and subdivergences · 0.81
Cites it as support 1 paper
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To further support this idea comes the remark that, when dealing with perturbative gravity, the core Hopf algebra is the pertinent Hopf algebra structure, because the one-loop graphs are the Hopf primitives (that is the graphs which have a trivial coproduct) [ref] .
Algebraic structures in quantum gravity · Introduction and motivation · 0.98
Cites it as background 5 papers
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They satisfy a certain system $(S)$ of combinatorial Dyson-Schwinger equation (briefly, SDSE), which uses combinatorial operators of insertion, and allows to inductively compute the homogeneous components of the Green functions, according to their loop number [ref] .
Mulitgraded Dyson-Schwinger systems · Introduction · 0.85
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The core Hopf algebra $H_core$ [ref] is based on the $ℚ$-vectorspace generated by connected bridgeless Feynman graphs and their disjoint unions.
Graph complexes and Feynman rules · The core Hopf algebra $H_core$ · 0.88
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The core Hopf algebra $H_core$ [ref] is based on the $ℚ$-vector space generated by connected bridgeless Feynman graphs.
Algebraic Interplay between Renormalization and Monodromy · The core Hopf algebra $H_core$ · 0.90
What it cites · 19 sentences without a confident label
Uses the method or tool of 3 papers
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These series in the coupling $g$ (series in $g$ with coefficients in the Hopf algebra) are fixpoints of equations formed by studying the Hochschild cohomology [ref] , $bB_+^j,m=0$, $m∈{2,4}$ of these Hopf algebras: X^4(g) = +∑_j>0 g^j B_+^j,4(X^4(g)(X^4(g)/(X^2(g))^2)^j) X^2(g) = -∑_j>0 g^j B_+^j,2(X^2(g)(X^4(g)/(X^2(g))^2)^j).
Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology · DSE in the core Hopf algebra · 0.82
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Applying the techniques of [ref] this is straightforward as we will report elsewhere [ref] .
Anatomy of a gauge theory · sub Hopf algebras and AdS/CFT · 0.97
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Applying the techniques of [ref] this is straightforward as we will report elsewhere [ref] .
Renormalization of gauge fields: A Hopf algebra approach · sub Hopf algebras and AdS/CFT · 0.97
Cites as background 3 papers
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See [ref] for notation and details.
Mixed Hodge Structures and Renormalization in Physics · The core Hopf algebra · 0.91
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The reader will have to consult [ref] for details.
Growth estimates for Dyson-Schwinger equations · DSE in the core Hopf algebra · 0.89
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The reader will have to consult [ref] for details.
Anatomy of a gauge theory · DSE in the core Hopf algebra · 0.89
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