Lois pré-Lie en interaction

Mathematics – Rings and Algebras

Scientific paper

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13 pages, in French. Improved version: confusion between two grafting laws removed, and operadic approach outlined

Scientific paper

D. Calaque, K. Ebrahimi-Fard and D. Manchon have recently defined a Hopf algebra by introducing a new coproduct on a commutative algebra of rooted forests. The space of primitive elements of the graded dual is endowed with a left pre-Lie product defined in terms of insertion of a tree inside another. In this work we prove a ``derivation'' relation between this pre-Lie structure and the left pre-Lie product defined by grafting.

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