Classification of the Finite-Dimensional Real Division Composition Algebras having a Non-Abelian Derivation Algebra
arXiv:1404.1896 · doi:10.1016/j.jalgebra.2015.07.025
Abstract
We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a quasi-description of a category, and using it to express the problem in terms of normal form problems for certain group actions on products of 3-spheres.