ALGEBRAIC COMBINATORICS Loïc Foissy, Frédéric Menous, Jean-Christophe Novelli & Jean-Yves Thibon Quadri-algebras, preLie algebras, and the Catalan family of Lie idempotents Volume 5, issue 4 (2022), p. 629-666. https://doi.org/10.5802/alco.224 © The author(s), 2022. This article is licensed under the CREATIVE COMMONS ATTRIBUTION 4.0 I NTERNATIONAL LICENSE. http://creativecommons.org/licenses/by/4.0/ Algebraic Combinatorics is published by The Combinatorics Consortium and is a member of the Centre Mersenne for Open Scientific Publishing www.tccpublishing.org www.centre-mersenne.org e-ISSN: 2589-5486