associator
Let A be a non-associative algebra over a field. The associator
of A, denoted by [,,], is a trilinear (http://planetmath.org/multilinear) map from A×A×A to A given by:
| [a,b,c]=(ab)c-a(bc). |
Just as the commutator measures how close an algebra
is to being commutative
, the associator measures how close it is to being associative. [,,]=0 identically iff A is associative.
References
- 1 R. D. Schafer, An Introduction on Nonassociative Algebras, Dover, New York (1995).
| 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 |