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
Zeitschrift:
Forum Mathematicum

ISSN: 0933-7741

Datum der Publikation: 2015

Ausgabe: 27

Nummer: 5

Seiten: 2691-2745

Art: Artikel

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

Andere Publikationen in: Forum Mathematicum

Zusammenfassung

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.