Abstract

We define Lie multiplication derivations of an arbitrary non-associative algebra A over any commutative ring and, following an approach due to K. McCrimmon, 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 dificulties in characteristic 3. We also show that octonion algebras over any commutative ring have only associator derivations.

Keywords

inner derivations, alternative algebras, derivation functors, composition algebras, automorphisms

Mathematical Subject Classification

Primary: 17D05

Secondary: 17A36, 17A45, 17B40

Authors