Autotopies and quasigroup identities: New aspects of non-associative division algebras
- Darpö, E. 2
- Pérez Izquierdo, J.M. 1
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1
Universidad de La Rioja
info
- 2 Mathematical Institute, 24-29 St Giles', Oxford, United Kingdom
ISSN: 0933-7741
Year of publication: 2015
Volume: 27
Issue: 5
Pages: 2691-2745
Type: Article
More publications in: Forum Mathematicum
Metrics
JCR (Journal Impact Factor)
- Year 2015
- Journal Impact Factor: 0.823
- Journal Impact Factor without self cites: 0.779
- Article influence score: 0.848
- Best Quartile: Q2
- Area: MATHEMATICS Quartile: Q2 Rank in area: 88/312 (Ranking edition: SCIE)
- Area: MATHEMATICS, APPLIED Quartile: Q2 Rank in area: 124/254 (Ranking edition: SCIE)
SCImago Journal Rank
- Year 2015
- SJR Journal Impact: 0.918
- Best Quartile: Q2
- Area: Mathematics (miscellaneous) Quartile: Q2 Rank in area: 100/418
- Area: Applied Mathematics Quartile: Q2 Rank in area: 146/555
Scopus CiteScore
- Year 2015
- CiteScore of the Journal : 1.5
- Area: Mathematics (all) Percentile: 71
- Area: Applied Mathematics Percentile: 41
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Abstract
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.