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Free Novikov algebras and the Hopf algebra of decorated multi-indices

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arxiv 2404.09899 v4 pith:5VA4YD7C submitted 2024-04-15 math.CO math.RA

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keywords algebraformulahopfmulti-indicescombinatorialcoproductdecoratedfree
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We propose a combinatorial formula for the coproduct in a Hopf algebra of decorated multi-indices that recently appeared in the literature, which can be briefly described as the graded dual of the enveloping algebra of the free Novikov algebra generated by the set of decorations. Similarly to what happens for the Hopf algebra of rooted forests, the formula can be written in terms of admissible cuts. We also prove a combinatorial formula for the extraction-contraction coproduct for undecorated multi-indices, in terms of a suitable notion of covering subforest.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Renormalising Feynman diagrams with multi-indices

    math-ph 2025-01 conditional novelty 7.0 of 10

    A Hopf algebra on multi-indices with an extraction-contraction coproduct reproduces BPHZ renormalisation and yields the renormalised measure's counterterms directly.

  2. Rough differential equations and planarly branched universal limit theorem

    math.PR 2024-12 conditional novelty 5.0 of 10

    The paper proves existence and uniqueness of solutions to rough differential equations driven by planarly branched rough paths for roughness 1/4 < alpha <= 1/3 via Banach's fixed point theorem.

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