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Loop of formal diffeomorphisms and Fàa di Bruno coloop bialgebra

Alessandra Frabetti 1 Ivan P Shestakov 
1 PSPM - Probabilités, statistique, physique mathématique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We consider a generalization of (pro)algebraic loops defined on general categories of algebras and the dual notion of a coloop bialgebra suitable to represent them as functors. Our main result is the proof that the natural loop of formal diffeomorphisms with associative coefficients is proalgebraic, and give a full description of the codivisions on its coloop bialgebra.This result provides a generalization of the Lagrange inversion formula to series with non-commutative coefficients, and a loop-theoretic explanation to the existence of the non-commutative Fàa di Bruno Hopf algebra. MSC: 20N05, 14L17, 18D35, 16T30
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Submitted on : Thursday, September 6, 2018 - 9:23:44 AM
Last modification on : Saturday, September 24, 2022 - 3:36:05 PM
Long-term archiving on: : Friday, December 7, 2018 - 1:02:06 PM

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  • HAL Id : hal-01849454, version 2
  • ARXIV : 1807.10477

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Alessandra Frabetti, Ivan P Shestakov. Loop of formal diffeomorphisms and Fàa di Bruno coloop bialgebra. 2018. ⟨hal-01849454v2⟩

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