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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.ORCID iD: 0000-0002-0182-6205
2011 (English)In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 125, no 2, 147-174 p.Article in journal (Refereed) Published
Abstract [en]

This is a study of morphisms in the category of finite-dimensional absolute valued algebras whose codomains have dimension four. We begin by citing and transferring a classification 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 cross-section.

Place, publisher, year, edition, pages
2011. Vol. 125, no 2, 147-174 p.
Keyword [en]
absolute valued algebra, division algebra, homomorphism, irreducibility, composition
National Category
URN: urn:nbn:se:uu:diva-172251DOI: 10.4064/cm125-2-2ISI: 000299619900002OAI: oai:DiVA.org:uu-172251DiVA: diva2:513913
Available from: 2012-04-04 Created: 2012-04-03 Last updated: 2015-03-31

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Alsaody, Seidon
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