Symmetric composition algebras over algebraic varieties
We assume 2 and 3 to be invertible elements in the base ring. The
structure of symmetric composition algebras over locally ringed spaces and thus
in particular over rings is investigated. Symmetric composition algebras are
constructed on the trace 0 elements of cubic alternative algebras over a
locally ringed space, if the global sections of the space contain a primitive
third root of unity, generalizing a method first presented by J. R. Faulkner.
We find examples of Okubo algebras over elliptic curves which cannot be made
into octonion algebras.
S. Pumpluen < susanne.pumpluen@nottingham.ac.uk >