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 AlgebraExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
Schafer, R. D. An Introduction to Nonassociative Algebras. New York: Dover, pp. 3-4, 1996.Referenced on Wolfram|Alpha
Derivation AlgebraCite this as:
Weisstein, Eric W. "Derivation Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DerivationAlgebra.html