Symmetric composition algebras over algebraic varieties (Q981652)

The study of symmetric composition algebras over locally ringed spaces is initiated in the paper under review, specially the structure of the symmetric composition algebras obtained from cubic alternative algebras. Hence an important part of the paper is devoted to the nontrivial task of extending the classical definitions over ground fields and the basic properties. The author obtains interesting examples of Okubo algebras over elliptic curves which do not have any isotopes which are octonion algebras, and of octonion algebras which appear as a Cayley-Dickson doubling of quaternion algebras but which do not contain any quadratic étale algebras.