Derivation Algebra

Let A be any algebra over a field F, and define a derivation of A as a linear operator D on A satisfying


for all x,y in A. Then the set D(A) of all derivations of A in a subspace of the associative algebra of all linear operators on A is a Lie algebra, called the derivation algebra.

See also

Lie Algebra

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Schafer, R. D. An Introduction to Nonassociative Algebras. New York: Dover, pp. 3-4, 1996.

Referenced on Wolfram|Alpha

Derivation Algebra

Cite this as:

Weisstein, Eric W. "Derivation Algebra." From MathWorld--A Wolfram Web Resource.

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