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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-2,
author = {Seidon Alsaody},
title = {Morphisms in the category of finite-dimensional absolute valued algebras},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {147-174},
zbl = {1254.17005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-2}
}
Seidon Alsaody. Morphisms in the category of finite-dimensional absolute valued algebras. Colloquium Mathematicae, Tome 122 (2011) pp. 147-174. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-2/