R. D. Schafer’s scientific contributions

... On the other hand, the octonions, made public by Cayley, are known to a general mathematical audience mostly for their automorphism group, associated with the simple Lie algebra of type G 2 . Moving further, the automorphism groups of the higher Cayley-Dickson algebras F = A 0 ⊂ A 1 ⊂ · · · were computed by Schafer [21], also see [11]. Namely, for n > 3, Aut(A n ) is a direct product of Aut(A n−1 ) and an abelian group. ...

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Loops with involution and the Cayley-Dickson doubling process