Real quadratic flexible division algebras
The authors generalize the Cayley-Dickson process to obtain all finite-dimensional real quadratic algebras from the complex numbers, quaternions, or Cayley numbers. This new process is called vectorial isotopy. A 16 parameter table is given for a class of eight-dimensional real quadratic, flexible algebras. Conditions on the parameters are given that determine which of these algebras are also division algebras, all of which are included in the 16 parameter family. The eight-dimensional algebras of the title are then classified up to isomorphism.
scientific article; zbMATH DE number 1331363
scientific article