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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

 (xy)D=(xD)y+x(yD)

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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References

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. https://mathworld.wolfram.com/DerivationAlgebra.html

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