Geodesic
Monomial Bases and Pre-Lie Structure for Free Lie Algebras
Journal of Lie theory, Tome 28 (2018) no. 4, pp. 941-967
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We construct a pre-Lie structure on the free Lie algebra L(E) generated by a set E, giving an explicit presentation of L(E) as the quotient of the free pre-Lie algebra TE, generated by the (non-planar) E-decorated rooted trees, by some ideal I. The main result in this paper is a description of Gröbner bases in terms of trees.
Classification : 05C05, 17D25, 17A50, 17B01
Mots-clés : Pre-Lie algebras, NAP algebras, free Lie algebras, monomial bases, rooted trees 
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     author = {M. J. H. Al-Kaabi and D. Manchon and F. Patras},
     title = {Monomial {Bases} and {Pre-Lie} {Structure} for {Free} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {941--967},
     year = {2018},
     volume = {28},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2018_28_4_JLT_2018_28_4_a3/}
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M. J. H. Al-Kaabi; D. Manchon; F. Patras. Monomial Bases and Pre-Lie Structure for Free Lie Algebras. Journal of Lie theory, Tome 28 (2018) no. 4, pp. 941-967. http://geodesic.mathdoc.fr/item/JLT_2018_28_4_JLT_2018_28_4_a3/