Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Multi-indices coproducts from ODEs to singular SPDEs
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by Yvain Bruned and Yingtong Hou;
Trans. Amer. Math. Soc. 378 (2025), 4903-4928
DOI: https://doi.org/10.1090/tran/9411
Published electronically: March 4, 2025

Abstract:

In this work, we introduce explicit formulae for the coproducts at play for multi-indices in ODEs and in singular SPDEs. The two coproducts described correspond to versions of the Butcher-Connes-Kreimer and extraction-contraction coproducts with multi-indices. The main idea is to use the fact that the coproducts are the adjoint of dual products for which one has an explicit simple formula. We are able to derive the explicit formulae via an inner product defined from a symmetry factor easily computable for multi-indices.
References
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Bibliographic Information
  • Yvain Bruned
  • Affiliation: Université de Lorraine, CNRS, IECL, F-54000 Nancy, France
  • MR Author ID: 952078
  • Email: yvain.bruned@univ-lorraine.fr
  • Yingtong Hou
  • Affiliation: Université de Lorraine, CNRS, IECL, F-54000 Nancy, France
  • ORCID: 0009-0001-6201-5684
  • Email: yingtong.hou@univ-lorraine.fr
  • Received by editor(s): June 7, 2024
  • Received by editor(s) in revised form: November 17, 2024, and December 21, 2024
  • Published electronically: March 4, 2025
  • Additional Notes: The first author was supported from the European Research Council (ERC) through the ERC Starting Grant Low Regularity Dynamics via Decorated Trees (LoRDeT), grant agreement No. 101075208.
  • © Copyright 2025 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 378 (2025), 4903-4928
  • MSC (2020): Primary 60H15, 60L70, 16T05
  • DOI: https://doi.org/10.1090/tran/9411