A construction method for Albert algebras over algebraic varieties

We assume 2 and 3 to be invertible elements in the base ring. We construct cubic Jordan algebras and, in particular, Albert algebras, over an integral proper scheme by providing the space of trace zero elements of a quartic Jordan algebra over a scheme with a new multiplication, generalizing a construction by B. N. Allison and J. R. Faulkner. In the process, admissible cubic algebras and pseudo-composition algebras over schemes are constructed and results on the structure of these algebras are obtained. Examples of admissible cubic algebras, Albert algebras and pseudo-composition algebras are constructed over elliptic curves.

S. Pumpluen < susanne.pumpluen@nottingham.ac.uk >