Ternary derivations of finite-dimensional real division algebras Original Research Article

We present for each nset membership, variant{1,2,4,8} a group acting on the set of all division algebra structures on image, and an invariant, the Lie algebra of ternary derivations, for this action. An exploration of these structures is conducted in terms of this new invariant obtaining simple descriptions of the division algebras involved. In the course of the investigation another family of algebras is considered, among them the algebra sl(4,F) of 4×4 traceless matrices with the symmetric product image shows an exceptional behavior.