Fine structures inside the PreLie operad

Chapoton, Frédéric

doi:10.1090/S0002-9939-2013-11655-2

Fine structures inside the PreLie operad
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by Frédéric Chapoton PDF

Proc. Amer. Math. Soc. 141 (2013), 3723-3737 Request permission

Abstract:

This article aims at a detailed analysis of the $\operatorname {PreLie}$ operad. We obtain a concrete description (as a morphism) of the relationship between the anticyclic structure of $\operatorname {PreLie}$ and the generators of $\operatorname {PreLie}$ as a $\operatorname {Lie}$-module, which was previously known only at the level of characters. Building on this, we obtain a surprising inclusion of the cyclic Lie module in the $\operatorname {PreLie}$ operad. We conjecture that the image of this inclusion generates an interesting free sub-operad.

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