Linear representations of formal loops

  1. Madariaga, S. 1
  2. Pérez-Izquierdo, J.M. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Linear and Multilinear Algebra

ISSN: 0308-1087

Year of publication: 2017

Volume: 65

Issue: 1

Pages: 79-112

Type: Article

DOI: 10.1080/03081087.2016.1168354 SCOPUS: 2-s2.0-84962359550 WoS: WOS:000389316000007 GOOGLE SCHOLAR

More publications in: Linear and Multilinear Algebra

Abstract

A representation of an object in a category is an abelian group in the corresponding comma category. In this paper, we derive the formulas describing linear representations of objects in the category of formal loops and formal loop homomorphisms and apply them to obtain a new approach to the representation theory of formal Moufang loops and Malcev algebras based on Moufang elements. Certain ‘non-associative Moufang symmetry’ of groups is revealed. © 2016 Informa UK Limited, trading as Taylor & Francis Group