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Classification of the four-dimensional power-commutative real division algebras
University of Oxford.ORCID iD: 0000-0001-9177-9774
Université Hassan II Mohammedia, Morocco.
2011 (English)In: Proceedings of the Royal Society of Edinburgh. Section A Mathematics, ISSN 0308-2105, E-ISSN 1473-7124, Vol. 141, no 6, 1207-1223 p.Article in journal (Refereed) Published
Abstract [en]

A classification of all four-dimensional power-commutative real division algebras is given. It is shown that every four-dimensional power-commutative realdivision algebra is an isotope of a particular kind of a quadratic division algebra. The description of such isotopes in dimensions four and eight is reduced to the description of quadratic division algebras. In dimension four, this leads to a complete and irredundant classification. As a special case, the finite-dimensionalpower-commutative real division algebras that have a unique non-zero idempotent are characterized.

Place, publisher, year, edition, pages
2011. Vol. 141, no 6, 1207-1223 p.
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-21719DOI: 10.1017/S0308210510000259ISI: 000298454000004Scopus ID: 2-s2.0-84857293837OAI: oai:DiVA.org:mdh-21719DiVA: diva2:652515
Available from: 2013-09-30 Created: 2013-09-30 Last updated: 2014-12-08Bibliographically approved

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Publisher's full textScopushttp://dx.doi.org/10.1017/S0308210510000259

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