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 >