A construction method for some real division algebras with su(3) as derivation algebra

We obtain a new family of eight-dimensional unital division algebras over a field F out of a separable quadratic field extension, a three-dimensional anisotropic hermitian form of determinant one and a scalar which lies in the field extension but is not contained in the base field. These algebras are not third-power associative.

Over the reals, this yields a family of division algebras with derivation algebra isomorphic to su(3) and automorphism group isomorphic to SU(3). The algebra is the direct sum of two one-dimensional modules and a six-dimensional irreducible su(3)-module. Two families of Albert isotopes of these algebras with the same characteristics are considered as well.

(Revised version 1 Jun 2010 and 19 Jul 2010)

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