Inner derivations of alternative algebras over commutative rings

We define multiplication derivations of an arbitrary non-associative algebra A over any commutative ring and, following McCrimmon (see preprint No. 252 on this server), describe them completely if A is alternative. Using this description, we propose a new definition of inner derivations for alternative algebras, among which Schafer's standard derivations and McCrimmon's associator derivations occupy a special place, the latter being particularly useful to resolve difficulties in characteristic 3. We also show that octonion algebras over any commutative ring have only associator derivations.

lopera.dvi (175K, final version 26 Sep 2008)
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(This paper has appeared in Algebra & Number Theory Vol. 2, No. 8 (2008), pp. 927--968.)

Ottmar Loos < ottmar.loos@uibk.ac.at >

Holger P. Petersson < holger.petersson@FernUni-Hagen.de >

Michel L. Racine < mracine@science.uottawa.ca >