The antipode of of a Com-PreLie Hopf algebra - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

The antipode of of a Com-PreLie Hopf algebra

Résumé

We study the compatibility between the antipode and the preLie product of a Com-PreLie Hopf algebra, that is to say a commutative Hopf algebra with a complementary preLie product, compatible with the product and the coproduct in a certain sense. An example of such a Hopf algebra is the Connes-Kreimer Hopf algebra, with the preLie product given by grafting of forests, extending the free preLie product of grafting of rooted trees. This compatibility is then used to study the antipode of the Connes-Moscovici subalgebra, which can be defined with the help of this preLie product. The antipode of the generators of this subalgebra gives a family of combinatorial coefficients indexed by partitions, which can be computed with the help of iterated harmonic sums.
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Dates et versions

hal-04595707 , version 1 (31-05-2024)

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  • HAL Id : hal-04595707 , version 1

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Loïc Foissy. The antipode of of a Com-PreLie Hopf algebra. 2024. ⟨hal-04595707⟩
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