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The double sign of a real division algebra of finite dimension greater than one
University of Oxford.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2011 (English)Report (Other academic)
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 E A \ {0} are shown to form an invariant of A, called its double sign. For each n E {2, 4, 8}, the double sign causes the category Dn 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 Dn.

Place, publisher, year, edition, pages
2011. , 12 p.
U.U.D.M. report / Uppsala University, Department of Mathematics, ISSN 1101-3591 ; 2011:18
Keyword [en]
Real division algebra, double sign, groupoid, block decomposition
National Category
Algebra and Logic
Research subject
URN: urn:nbn:se:uu:diva-160628OAI: diva2:451972
Available from: 2011-10-28 Created: 2011-10-27 Last updated: 2012-02-16Bibliographically approved

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