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Dissident maps on the seven-dimensional Euclidean space
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2003 (English)In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 97, 251-276 p.Article in journal (Refereed) Published
Abstract [en]

Our article contributes to the classification of dissident maps on R7, which in turn contributes to the classification of 8-dimensional real division algebras. We study two large classes of dissident maps on R7. The first class is formed by all composed dissident maps, obtained from a vector product on R7 by composition with a definite endomorphism. The second class is formed by all doubled dissident maps, obtained as the purely imaginary parts of the structures of those 8-dimensional real quadratic division algebras which arise from a 4-dimensional real quadratic division algebra by doubling. For each of these two classes we exhibit a complete (but redundant) classification, given by a 49-parameter family of composed dissident maps and a 9-parameter family of doubled dissident maps respectively. The intersection of these two classes forms one isoclass of dissident maps only, namely the isoclass consisting of all vector products on R7.

Place, publisher, year, edition, pages
2003. Vol. 97, 251-276 p.
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-22144DOI: 10.4064/cm97-2-10OAI: oai:DiVA.org:uu-22144DiVA: diva2:49917
Available from: 2007-01-11 Created: 2007-01-11 Last updated: 2017-12-07Bibliographically approved

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Dieterich, ErnstLindberg, Lars

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