Séminaire Lotharingien de Combinatoire, B71b (2014), 19 pp.
Mahdi J. Hasan Al-Kaabi
Monomial Bases for Free Pre-Lie Algebras
We study the concept of a free pre-Lie algebra generated
by a (non-empty) set. We review the construction by Agrachev and
Gamkrelidze [J. Sov. Math. 17 (1981), 1650-1675]
of monomial bases in free pre-Lie algebras. We
describe the matrix of the monomial basis vectors in terms of the
rooted trees basis exhibited by Chapoton and Livernet
[Internat. Math. Res. Notices 8 (2001), 395-408].
Also, we show that this matrix is unipotent, and we find
an explicit expression for its coefficients, which uses a similar
procedure for the free magmatic algebra at the level of planar rooted
trees which has been suggested by Ebrahimi-Fard and Manchon.
Received: October 17, 2013.
Revised: January 22, 2014.
Accepted: January 29, 2014.
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