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

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...

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Bibliographic Details
Published in:Algebraic combinatorics 2022-01, Vol.5 (4), p.629-666
Main Authors: Foissy, Loïc, Menous, Frédéric, Novelli, Jean-Christophe, Thibon, Jean-Yves
Format: Article
Language:English
Subjects:
Mathematics
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Summary: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.
ISSN:2589-5486
2589-5486
DOI:10.5802/alco.224