Lie's correspondence for commutative automorphic formal loops
- Grishkov, A. 23
- Pérez-Izquierdo, J.M. 1
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1
Universidad de La Rioja
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2
Universidade de São Paulo
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3
Omsk State University
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ISSN: 0024-3795
Year of publication: 2018
Volume: 544
Pages: 460-501
Type: Article
More publications in: Linear Algebra and Its Applications
Related Projects
2014/00067/001
Abstract
We develop Lie's correspondence for commutative automorphic formal loops, which are natural candidates for non-associative abelian groups, to show how linearization techniques based on Hopf algebras can be applied to study non-linear structures. Over fields of characteristic zero, we prove that the category of commutative automorphic formal loops is equivalent to certain category of Lie triple systems. An explicit Baker–Campbell–Hausdorff formula for these loops is also obtained with the help of formal power series with coefficients in the algebra of 3 by 3 matrices. Our formula is strongly related to the function [Formula presented]. © 2018 Elsevier Inc.