Journal of Lie Theory

no. 4
Monomial Bases and Pre-Lie Structure for Free Lie Algebras
Mahdi J. Hasan Al-Kaabi1; Dominique Manchon2; Frédéric Patras3
1Mathematics Department, College of Science, Mustansiriyah University, Palestine Street, Baghdad, Iraq
2LMBP, CNRS-UMR6620, Université Clermont-Auvergne, 3 place Vasarély, 63178 Aubière, France
3Laboratoire J. A. Dieudonné, UMR CNRS-UNS N7351, Université de Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 2, France
Journal of Lie Theory, Volume 28 (2018) no. 4, pp. 941-967
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.
DOI: 10.5802/jolt.1035
Classification: 05C05, 17D25, 17A50, 17B01
Keywords: Pre-Lie algebras, NAP algebras, free Lie algebras, monomial bases, rooted trees

Mahdi J. Hasan Al-Kaabi  1 ; Dominique Manchon  2 ; Frédéric Patras  3

1 Mathematics Department, College of Science, Mustansiriyah University, Palestine Street, Baghdad, Iraq
2 LMBP, CNRS-UMR6620, Université Clermont-Auvergne, 3 place Vasarély, 63178 Aubière, France
3 Laboratoire J. A. Dieudonné, UMR CNRS-UNS N7351, Université de Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 2, France 
Mahdi J. Hasan Al-Kaabi; Dominique Manchon; Frédéric Patras. Monomial Bases and Pre-Lie Structure for Free Lie Algebras. Journal of Lie Theory, Volume 28 (2018) no. 4, pp. 941-967. doi: 10.5802/jolt.1035
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     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},
     doi = {10.5802/jolt.1035},
     zbl = {1453.17019},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1035/}
}
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