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Morphisms in the Category of Finite Dimensional Absolute Valued Algebras
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]

This is a study of morphisms in the category of nite dimensional absolute valued algebras, whose codomains have dimension four. We begin by citing and transferring a classication of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for the morphisms from two-dimensional algebras we describe the orbits under the actions of the automorphism groups involved. Parts of these descriptions rely on a suitable choice of a cross-section of four-dimensional absolute valued algebras, and we thus end by providing an explicit means of transferring these results to algebras outside this crosssection.

Place, publisher, year, edition, pages
Uppsala: Uppsala University, Department of Mathematics , 2011. , 23 p.
U.U.D.M. report / Uppsala University, Department of Mathematics, ISSN 1101-3591 ; 2011:13
National Category
Algebra and Logic
Research subject
URN: urn:nbn:se:uu:diva-158198OAI: diva2:438134
Available from: 2011-10-04 Created: 2011-09-01 Last updated: 2012-02-16Bibliographically approved

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