A CLASSIFICATION THEOREM FOR ALBERT ALGEBRAS

Let k be a field whose characteristic is different from 2 and 3 and le t L/k be a quadratic extension. In this paper we prove that for a fixe d, degree 3 central simple algebra B over L with an involution sigma o f the second kind over k, the Jordan algebra J(B, sigma, u, mu), obtai ned through Tits' second construction is determined up to isomorphism by the class of (u, mu) in H-1(k, SU(B, sigma)), thus settling a quest ion raised by Petersson and Racine. As a consequence, we derive a ''Sk olem Noether'' type theorem for Albert algebras. We also show that the cohomological invariants determine the isomorphism class of J(B, sigm a, u, mu), if (B, sigma) is fixed.