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Let $A$ be a non-associative algebra over a field. The associator of $A$ denoted by $[\ , , ]$ is a trilinear map from $A\times A\times A$ 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.
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- R. D. Schafer, An Introduction on Nonassociative Algebras, Dover, New York (1995).
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"associator" is owned by CWoo.
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Cross-references: iff, associative, commutative, algebra, commutator, map, field, non-associative algebra
There are 9 references to this entry.
This is version 7 of associator, born on 2004-10-10, modified 2006-10-02.
Object id is 6348, canonical name is Associator.
Accessed 3428 times total.
Classification:
| AMS MSC: | 17A01 (Nonassociative rings and algebras :: General nonassociative rings :: General theory) |
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Pending Errata and Addenda
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