Associator

For an algebra A, the associator is the trilinear map A×A×A->A given by

(x,y,z)=(xy)z-x(yz).

The associator is identically zero iff A is associative.

See also

Alternative Algebra, Commutator, Power Associative Algebra

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References

Schafer, R. D. An Introduction to Nonassociative Algebras. New York: Dover, p. 13, 1996.

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Cite this as:

Weisstein, Eric W. "Associator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Associator.html

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