Morphisms in the category of finite-dimensional absolute valued algebras

Seidon Alsaody¹

¹ Department of Mathematics Uppsala University P.O. Box 480 SE-75106 Uppsala, Sweden

Colloquium Mathematicum, Tome 125 (2011) no. 2, pp. 147-174.

Résumé

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.

Détail

DOI : 10.4064/cm125-2-2

Keywords: study morphisms category finite dimensional absolute valued algebras whose codomains have dimension begin citing transferring classification equivalent category thereafter complete description morphisms one dimensional algebras partly via solutions real polynomials complete explicit description morphisms two dimensional algebras account reducibility morphisms morphisms two dimensional algebras describe orbits under actions automorphism groups involved parts these descriptions rely suitable choice cross section four dimensional absolute valued algebras end providing explicit means transferring these results algebras outside cross section