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Abstract
Associated to any eight-dimensional non-unital composition algebra with associative norm, there are outer automorphisms of order 3 of the corresponding spin group, such tiat the fixed subgroup is the automorphism group of the composition algebra. Over fields of characteristic ≠ 3 these are simple algebraic groups of types G 2 or A 2, related respectively to the para-octonion and the Okubo algebras
A connection between the Okubo algebras over fields of characteristic 3 with some simple noncommutative Jordan algebras will be used to compute explicitly the automorphism groups and Lie algebras of derivations of these algebras. In contrast to the other characteristics, ths groups will no longer be of type A 2 and will either be trivial or contain a large unipotent radical.
*Supported by the spanish DGICYT (Pb 94-1311-003-03)and by the Universidad de La Rioja(API-97/B05 and API-98/B15).
*Supported by the spanish DGICYT (Pb 94-1311-003-03)and by the Universidad de La Rioja(API-97/B05 and API-98/B15).
Notes
*Supported by the spanish DGICYT (Pb 94-1311-003-03)and by the Universidad de La Rioja(API-97/B05 and API-98/B15).