The free-operad identification conjecture for the cyclic Lie sub-operad of PreLie

Let PreLie\operatorname{PreLie} be the PreLie operad, let CycLie\operatorname{CycLie} be the cyclic Lie module, and let MM be the sub-operad generated by the image of CycLie\operatorname{CycLie} under the map λ\lambda. Let FreeOp(CycLie)\operatorname{FreeOp}(\operatorname{CycLie}) denote the free operad on CycLie\operatorname{CycLie}. The free-operad identification conjecture. The sub-operad MM is isomorphic to the free operad on CycLie\operatorname{CycLie}, namely

FreeOp(CycLie)M.\operatorname{FreeOp}(\operatorname{CycLie})\simeq M.

This asserts that there are no further operadic relations among the generators supplied by the cyclic Lie module; the source gives no resolution.

Sources & referencesView supporting material

Primary source

Frédéric Chapoton, “Fine structures inside the PreLie operad”, arXiv:1010.3176 (2010).

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