Faà di Bruno Hopf algebras
- Héctor Figueroa 1
- Várilly, Joseph C. 1
- Gracia-Bondía, José M. 2
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1
Universidad de Costa Rica
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2
Universidad de Zaragoza
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ISSN: 0034-7426
Year of publication: 2022
Volume: 56
Issue: 1
Pages: 1-12
Type: Article
More publications in: Revista Colombiana de Matemáticas
Abstract
This is a short review on the Faà 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 Faà di Bruno formulas with the theory of set partitions is developed in some detail.
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