Algebra & Number Theory
- Algebra Number Theory
- Volume 2, Number 8 (2008), 927-968.
Inner derivations of alternative algebras over commutative rings
We define Lie multiplication derivations of an arbitrary non-associative algebra over any commutative ring and, following an approach due to K. McCrimmon, describe them completely if 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 . We also show that octonion algebras over any commutative ring have only associator derivations.
Algebra Number Theory, Volume 2, Number 8 (2008), 927-968.
Received: 6 April 2008
Revised: 26 September 2008
Accepted: 26 October 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 17D05: Alternative rings
Secondary: 17A36: Automorphisms, derivations, other operators 17A45: Quadratic algebras (but not quadratic Jordan algebras) 17B40: Automorphisms, derivations, other operators
Loos, Ottmar; Petersson, Holger; Racine, Michel. Inner derivations of alternative algebras over commutative rings. Algebra Number Theory 2 (2008), no. 8, 927--968. doi:10.2140/ant.2008.2.927. https://projecteuclid.org/euclid.ant/1513805230