Associated to any eight-dimensional non-unital composition algebra with ass
ociative norm, there are outer automorphisms of order 3 of the correspondin
g spin group, such that the fixed subgroup is the automorphism group of the
composition algebra, Over fields of characteristic not equal 3 these are s
imple algebraic groups of types G(2) or A(2), related respectively to the p
ara-octonion and the Okubo algebras.
A connection between the Okubo algebras over fields of characteristic 3 wit
h some simple noncommutative Jordan algebras will be used to compute explic
itly the automorphism groups and Lie algebras of derivations of these algeb
ras. In contrast to the other characteristics, the groups will no longer be
of type A(2) and will either be trivial or contain a large unipotent radic
al.