Autotopies and quasigroup identities: New aspects of non-associative division algebras

  1. Darpö, E. 2
  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 Mathematical Institute, 24-29 St Giles', Oxford, United Kingdom
Revista:
Forum Mathematicum

ISSN: 0933-7741

Año de publicación: 2015

Volumen: 27

Número: 5

Páginas: 2691-2745

Tipo: Artículo

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DOI: 10.1515/FORUM-2012-0087 SCOPUS: 2-s2.0-84941066543 WoS: WOS:000360855700007 GOOGLE SCHOLAR

Otras publicaciones en: Forum Mathematicum

Objetivos de desarrollo sostenible

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Álgebras, triples y lazos relacionados con Geometría y Supermetría

2011/00007/001

Resumen

In this article, we explore new aspects in the classification of non-associative division algebras. By a detailed study of the representations of the Lie group of autotopies of real division algebras we show that, if the group of autotopies has a sufficiently rich structure, then the algebra is isotopic to one of the classical real division algebras. This turns out to be the case for large classes of real division algebras, including many that are defined by identities. In several cases, a classification up to isomorphism can be worked out from this information. © 2015 by De Gruyter.