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

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

  2. 2 Mathematical Institute, 24-29 St Giles', Oxford, United Kingdom
Forum Mathematicum

ISSN: 0933-7741

Year of publication: 2015

Volume: 27

Issue: 5

Pages: 2691-2745

Type: Article

Export: RIS
DOI: 10.1515/forum-2012-0087 SCOPUS: 2-s2.0-84941066543 WoS: 000360855700007 GOOGLE SCHOLAR


Cited by

  • Scopus Cited by: 2 (14-07-2021)

Journal Citation Reports

  • Year 2015
  • Journal Impact Factor: 0.823
  • Best Quartile: Q2
  • Area: MATHEMATICS, APPLIED Quartile: Q2 Rank in area: 124/254 (Ranking edition: SCIE)
  • Area: MATHEMATICS Quartile: Q2 Rank in area: 88/312 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2015
  • SJR Journal Impact: 0.918
  • Best Quartile: Q2
  • Area: Applied Mathematics Quartile: Q2 Rank in area: 146/545
  • Area: Mathematics (miscellaneous) Quartile: Q2 Rank in area: 98/419


  • Year 2015
  • CiteScore of the Journal : 1.5
  • Area: Mathematics (all) Percentile: 71
  • Area: Applied Mathematics Percentile: 41


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.