Lie's correspondence for commutative automorphic formal loops

  1. Grishkov, A. 23
  2. Pérez-Izquierdo, J.M. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidade de São Paulo
    info

    Universidade de São Paulo

    São Paulo, Brasil

    ROR https://ror.org/036rp1748

  3. 3 Omsk State University
    info

    Omsk State University

    Omsk, Rusia

    ROR https://ror.org/01k6vxj52

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Zeitschrift:
Linear Algebra and Its Applications

ISSN: 0024-3795

Datum der Publikation: 2018

Ausgabe: 544

Seiten: 460-501

Art: Artikel

DOI: 10.1016/J.LAA.2018.01.028 SCOPUS: 2-s2.0-85041442633 WoS: WOS:000428002500021 GOOGLE SCHOLAR

Andere Publikationen in: Linear Algebra and Its Applications

Projekte im Zusammenhang

Álgebra y superálgebras de Lie. Teoría de Lie no asociativa

2014/00067/001

Zusammenfassung

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.