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The double sign of a real division algebra of finite dimension greater than one
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2012 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 285, no 13, 1635-1642 p.Article in journal (Refereed) Published
Abstract [en]

For any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by an element a is an element of A\{0} are shown to form an invariant of A, called its double sign. For each n is an element of {2, 4, 8}, the double sign causes the category D-n of all n-dimensional real division algebras to decompose into four blocks. The structures of these blocks are closely related, and their relationship is made precise for a sample of full subcategories of D-n.

Place, publisher, year, edition, pages
2012. Vol. 285, no 13, 1635-1642 p.
Keyword [en]
Real division algebra, double sign, groupoid, block decomposition, msc (2010) 17A35, 18B40, 54C05
National Category
Algebra and Logic
URN: urn:nbn:se:uu:diva-179384DOI: 10.1002/mana.201100189ISI: 000308643300008OAI: oai:DiVA.org:uu-179384DiVA: diva2:544464
Available from: 2012-08-14 Created: 2012-08-14 Last updated: 2012-10-25Bibliographically approved

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Dieterich, Ernst
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