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Derivations and
Cayley derivations of generalized Cayley-Dickson algebras
Kevin Mor McCrimmon |
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Vol. 117 (1985), No. 1, 163–182
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Abstract |
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The Cayley-Dickson doubling process can be continued past the quaternions and octonions to obtain an infinite series of algebras of dimension 2n. After n = 3 these algebras are no longer composition algebras. R. D. Schafer established the surprising result that the derivation algebras stop growing at n = 3. Schafer’s proof assumed the scalars were a field of characteristic ≠2,3. In this paper we will give a different proof of his result which works for arbitrary rings of scalars, making use of the concept of a Cayley derivation. |
Mathematical Subject Classification 2000
Primary: 17A15
Secondary: 17B60
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Milestones
Received: 18 April 1983
Published: 1 March 1985
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Authors |
| Kevin Mor McCrimmon | |
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