Monomial bases for free pre-Lie algebras
type: Item
instance of: scholarly article
title: Monomial bases for free pre-Lie algebras
zbMATH Open document ID: 1303.17023
published in: Séminaire Lotharingien de Combinatoire
publication date: 2014-08-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/1309.4243
full work available at URL: s71mahdi.html
review text: As shown by \textit{F. Chapoton} and \textit{M. Livernet} [Int. Math. Res. Not. 2001, No. 8, 395--408 (2001; Zbl 1053.17001)], the free pre-Lie algebra generated by a nonempty set admits a basis given by the set of rooted trees which internal vertices are decorated by elements of the generating set. However, this is not a monomial basis. The present text considers monomial bases of free pre-Lie algebras, such that the leading terms, according to the filtration by the tree-grounded degree, give back the basis of rooted trees. It is shown that these bases are in one-to-one correspondence with sections of the canonical projection from planar rooted trees to rooted trees. Moreover, the matrix of such a monomial basis, expressed in the basis of rooted trees, is unipotent; an explicit formula is given for its coefficients.
Mathematics Subject Classification ID: 17D25
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 6335255
zbMATH Keywords: Prelie algebras
zbMATH Keywords: monomial basis
zbMATH Keywords: rooted trees
reviewed by: Loïc Foissy
describes a project that uses: OEIS
MaRDI profile type: Publication
arXiv ID: 1309.4243
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description: scientific article; zbMATH DE number 6335255