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
Datum der Publikation: 2015
Ausgabe: 27
Nummer: 5
Seiten: 2691-2745
Art: Artikel
Andere Publikationen in: Forum Mathematicum
Projekte im Zusammenhang
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.