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Journal Articles Algebraic Combinatorics Year : 2022

Quadri-algebras, preLie algebras, and the Catalan family of Lie idempotents

Abstract

We compute the expansion of the Catalan family of Lie idempotents introduced in [Menous et al., Adv. Applied Math. 51 (2013), 177-22] on the PBW basis of the Lie module. It is found that the coefficient of a tree depends only on its number of left and right internal edges. In particular, the Catalan idempotents belong to a preLie algebra based on naked binary trees, of which we identify several Lie and preLie subalgebras.

Dates and versions

hal-03621275 , version 1 (28-03-2022)

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Loïc Foissy, Frédéric Menous, Jean-Christophe Novelli, Jean-Yves Thibon. Quadri-algebras, preLie algebras, and the Catalan family of Lie idempotents. Algebraic Combinatorics, 2022, pp.629-666. ⟨10.5802/alco.224⟩. ⟨hal-03621275⟩
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