S Invariants of Finite Dimensional Real Division Algebras.

Finite dimensional real division algebras are examined under the permutation of their structure constants. It is noted that there is only one finite-dimensional real flexible division algebras with an automorphism group isomorphic to S . We show that the 8-dimensional real division algebras with derivation algebra g are isotopic under all permutations of the structure constants. Being a composition algebra is preserved under all permutations. We simultaneously derive information about the quaternion division algebras as subalgebras of the eight dimensional algebras. Finally, a division algebra with derivation algebra $${su(2)\oplus su(2)}$$ is looked at under the actions of S . The quaternion, octonion and Okubo algebras are special cases of our results. [ABSTRACT FROM AUTHOR]