Читать книгу Algebra and Applications 2 - Группа авторов - Страница 37

We adopt the notations of section 1.5. The sum of the partial compositions yields a right pre-Lie algebra structure on the free -algebra with one generator, more precisely on , namely:

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Following Chapoton (2002), we can consider the pro-unipotent group associated with the completion of the pre-Lie algebra for the filtration induced by the grading. More precisely, Chapoton’s group is given by the elements , such that g₁ ≠ 0, whereas is the subgroup of formed by elements g, such that g₁ = e.

Any element gives rise to an n-ary operation , and for any , we have¹ (Manchon and Saidi 2011):

[1.78]