Abstract

FIGUEROA, Héctor; VARILLY, Joseph C.  and  GRACIA-BONDIA, José M.. Faà di Bruno Hopf algebras. Rev.colomb.mat. [online]. 2022, vol.56, n.1, pp.1-12.  Epub Jan 02, 2024. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v56n1.105611.

This is a short review on the Faá di Bruno formulas, implementing composition of real-analytic functions, and a Hopf algebra associated to such formulas. This structure provides, among several other things, a short proof of the Lie-Scheffers theorem, and relates the Lagrange inversion formulas with antipodes. It is also the maximal commutative Hopf subalgebra of the one used by Connes and Moscovici to study diffeomorphisms in a noncommutative geometry setting. The link of Faa di Bruno formulas with the theory of set partitions is developed in some detail.

Keywords : Faá di Bruno formula; Hopf algebras; partitions.

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