Combinatorics of pre-Lie products sharing a Lie bracket

Published 11 Sep 2023 in math.QA, math.CO, and math.RA | (2309.05552v3)

Abstract: We study in detail the operad controlling several pre-Lie algebra structures sharing the same Lie bracket. Specifically, we show that this operad admits a combinatorial description similar to that of Chapoton and Livernet for the pre-Lie operad, and that it has many of the remarkable algebraic properties of the pre-Lie operad.

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Paul Laubie

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