Morphisms in the Category of Finite Dimensional Absolute Valued Algebras
2011 (English)Report (Other academic)
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
Algebra and Logic
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-158198OAI: oai:DiVA.org:uu-158198DiVA: diva2:438134