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Autotopies and quasigroup identities: new aspects of non-associative division algebras
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mathematical Institute, St Giles', Oxford, United Kingdom. (Mathematics and Applied Mathematics)ORCID iD: 0000-0001-9177-9774
Universidad de la Rioja, Spain.
2015 (English)In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 27, no 5, p. 2691-2745Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
De Gruyter , 2015. Vol. 27, no 5, p. 2691-2745
National Category
Algebra and Logic Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-21740DOI: 10.1515/forum-2012-0087OAI: oai:DiVA.org:mdh-21740DiVA, id: diva2:652522
Available from: 2013-09-30 Created: 2013-09-30 Last updated: 2017-12-29Bibliographically approved

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Darpö, Erik

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