Morphisms in the category of finite-dimensional absolute valued algebras

Seidon Alsaody. "Morphisms in the category of finite-dimensional absolute valued algebras." Colloquium Mathematicae 125.2 (2011): 147-174. <http://eudml.org/doc/283559>.

@article{SeidonAlsaody2011,
abstract = {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.},
author = {Seidon Alsaody},
journal = {Colloquium Mathematicae},
keywords = {absolute valued algebra; division algebra; homomorphism; irreducible},
language = {eng},
number = {2},
pages = {147-174},
title = {Morphisms in the category of finite-dimensional absolute valued algebras},
url = {http://eudml.org/doc/283559},
volume = {125},
year = {2011},
}

TY - JOUR
AU - Seidon Alsaody
TI - Morphisms in the category of finite-dimensional absolute valued algebras
JO - Colloquium Mathematicae
PY - 2011
VL - 125
IS - 2
SP - 147
EP - 174
AB - 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.
LA - eng
KW - absolute valued algebra; division algebra; homomorphism; irreducible
UR - http://eudml.org/doc/283559
ER -