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

2020/05/18 by Loïc Foissy, Frédéric Menous, Foissy, Loïc +5
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.08888

openalex publication_date 2020/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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