Real non-unital division algebras with su(3) as derivation algebra

We obtain a family of non-unital eight-dimensional division algebras over a field F out of a separable quadratic field extension S of F, a three-dimensional anisotropic hermitian form over S of determinant one, and three invertible elements c,d,e∈S. These algebras contain a four-dimensional subalgebra which can be viewed as a generalization of a (nonassociative) quaternion algebra. The four-dimensional algebras are studied independently.Over R, this construction can be used to generate division algebras with derivation algebra isomorphic to su(3), which are the direct sum of two one-dimensional modules and a six-dimensional irreducible su(3)-module. Albert isotopes with derivation algebra isomorphic to su(3) are considered briefly as well.