#### Vol. 2, No. 8, 2008

 Recent Issues
 The Journal Cover Editorial Board Editors' Addresses Editors' Interests About the Journal Scientific Advantages Submission Guidelines Submission Form Subscriptions Editorial Login Contacts Author Index To Appear ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print)
Inner derivations of alternative algebras over commutative rings

### Ottmar Loos, Holger P. Petersson and Michel L. Racine

Vol. 2 (2008), No. 8, 927–968
##### 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 difficulties in characteristic $3$. We also show that octonion algebras over any commutative ring have only associator derivations.

 Erhard Neher zum 60. Geburtstag gewidmet
##### Keywords
inner derivations, alternative algebras, derivation functors, composition algebras, automorphisms
##### Mathematical Subject Classification 2000
Primary: 17D05
Secondary: 17A36, 17A45, 17B40