Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 43 min ago
Peer-reviewedCC BY 4.0Algebraic Combinatorics

Combinatorics of pre-Lie products sharing the same Lie bracket

  • Paul Laubie1
  1. 1University of Strasbourg and CNRS, Institut de Recherche Mathématique Avancée, UMR 7501, 67000 Strasbourg CEDEX, Strasbourg, France
Open at sourcePDFDOICite

Abstract

We study in detail the operad controlling several pre-Lie products sharing the same Lie bracket. We show that this operad admits a combinatorial description similar to that of Chapoton and Livernet for the pre-Lie operad, namely the underlying species of the operad controlling two pre-Lie products sharing the same Lie bracket is the species of rooted Greg trees, which are rooted trees with black and white vertices such that the black vertices have at least two children, and the composition is the insertion. Moreover, we show that it has many of the remarkable algebraic properties of the pre-Lie operad.

Related

  1. Ricci flows and bracket flows on twisted principal bundles
    Henry Wood
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  2. Lie bracket approximations of RMSprop for Extremum Seeking Control
    Victoria Grushkovskaya, Christian Ebenbauer
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  3. Sets whose differences avoid a bracket quadratic
    Khalid Younis
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. Stochastic Lie-Bracket Approximations for Zeroth-Order Optimization on Manifolds
    Mahmoud Abdelgalil, Miroslav Krstic, Jorge I. Poveda
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  5. Combining Exponential and Polynomial Convergence Rates for Accelerated Extremum Seeking: A High-Order Lie Bracket Approach
    Victoria Grushkovskaya, Sameh Eisa
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@article{laubie2026combinatorics,
  title = {{Combinatorics of pre-Lie products sharing the same Lie bracket}},
  author = {Paul Laubie},
  journal = {Algebraic Combinatorics},
  year = {2026},
  month = oct,
  doi = {10.5802/alco.508},
  url = {https://alco.centre-mersenne.org/articles/10.5802/alco.508/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Combinatorics of pre-Lie products sharing the same Lie bracket
AU  - Paul Laubie
PY  - 2026
DA  - 2026/10/27
JO  - Algebraic Combinatorics
DO  - 10.5802/alco.508
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.508/
AB  - We study in detail the operad controlling several pre-Lie products sharing the same Lie bracket. We show that this operad admits a combinatorial description similar to that of Chapoton and Livernet for the pre-Lie operad, namely the underlying species of the operad controlling two pre-Lie products sharing the same Lie bracket is the species of rooted Greg trees, which are rooted trees with black and white vertices such that the black vertices have at least two children, and the composition is the insertion. Moreover, we show that it has many of the remarkable algebraic properties of the pre-Lie operad.
SN  - 2589-5486
ER  -