Morphisms in the category of finite-dimensional absolute valued algebras

Volume 125 / 2011

Seidon Alsaody Colloquium Mathematicum 125 (2011), 147-174 MSC: Primary 17A35; Secondary 17A80. DOI: 10.4064/cm125-2-2


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.


  • Seidon AlsaodyDepartment of Mathematics
    Uppsala University
    P.O. Box 480
    SE-75106 Uppsala, Sweden

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