Let A be a non-associative algebra over a field. The associatorMathworldPlanetmath of A, denoted by [,,], is a trilinear ( map from A×A×A to A given by:


Just as the commutatorMathworldPlanetmathPlanetmath measures how close an algebraMathworldPlanetmathPlanetmathPlanetmath is to being commutativePlanetmathPlanetmathPlanetmath, the associator measures how close it is to being associative. [,,]=0 identically iff A is associative.


Title associator
Canonical name Associator
Date of creation 2013-03-22 14:43:21
Last modified on 2013-03-22 14:43:21
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 10
Author CWoo (3771)
Entry type Definition
Classification msc 17A01
Related topic AlternativeAlgebra
Related topic PowerAssociativeAlgebra
Related topic FlexibleAlgebra
Related topic Commutator
Defines anti-associative