Isotopes of Hurwitz Algebras

Abstract

We study the class of all algebras that are isotopic to a Hurwitz algebra. Isomorphism classes of such algebras are shown to correspond to orbits of a certain group action. A complete, geometrically intuitive description of the category of isotopes of Hamilton's quaternions is given. As an application, we demonstrate how some results concerning the classification of finite-dimensional composition algebras can be deduced from our general results.