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Search: MSC category 18G40 ( Spectral sequences, hypercohomology [See also 55Txx] )

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1. CMB 2010 (vol 53 pp. 425)

Chapoton, Frédéric
 Free Pre-Lie Algebras are Free as Lie Algebras We prove that the \$\mathfrak{S}\$-module \$\operatorname{PreLie}\$ is a free Lie algebra in the category of \$\mathfrak{S}\$-modules and can therefore be written as the composition of the \$\mathfrak{S}\$-module \$\operatorname{Lie}\$ with a new \$\mathfrak{S}\$-module \$X\$. This implies that free pre-Lie algebras in the category of vector spaces, when considered as Lie algebras, are free on generators that can be described using \$X\$. Furthermore, we define a natural filtration on the \$\mathfrak{S}\$-module \$X\$. We also obtain a relationship between \$X\$ and the \$\mathfrak{S}\$-module coming from the anticyclic structure of the \$\operatorname{PreLie}\$ operad. Categories:18D50, 17B01, 18G40, 05C05

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