Morphisms in the category of finite-dimensional absolute valued algebras

• Autorzy: Seidon Alsaody
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 17A80: Valued algebras
• 17A35: Division algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 125
• Numer: 2
• Strony: 147-174

Daty

wydano

2011

Twórcy

autor

Seidon Alsaody

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

Identyfikatory

DOI

10.4064/cm125-2-2