How to obtain division algebras from twisted Cayley-Dickson
doublings
We change the order of the factors in the classical Cayley-Dickson
doubling process and investigate the eight-dimensional algebras
obtained when doubling a quaternion algebra using this twisted
multiplication. We also allow the scalar c used in the doubling
process to be an invertible element in the quaternion algebra. By
changing the place of c inside the multiplication we then obtain
different families of algebras. We give conditions when these
algebras are division over a given base field.
S. Pumpluen < susanne.pumpluen@nottingham.ac.uk >