Associator

Summary

The associator of three elements $x, y, z$ of a nonassociative algebra is $(x, y, z) = (xy)z - x(yz)$. It measures how far the product is from being associative, in the same way as the commutator measures how far it is from being commutative. Many classes of nonassociative algebras are defined by conditions on the associator, such as alternative algebras and flexible algebras.