Classification of the finite-dimensional real division composition algebras having a non-Abelian derivation algebra

摘要

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. (C) 2015 Elsevier Inc. All rights reserved.