Derivation

Summary

A derivation is a linear map on an algebra that satisfies the product rule $D(ab) = D(a) b + a D(b)$, see the definition. It is the algebraic form of the derivative, and it makes sense without limits. Derivations are basic in differential algebra, algebraic geometry and Lie theory. The derivations of a Lie algebra obey the same rule for the Lie bracket. The commutator of two derivations is again a derivation, so the derivations of an algebra form a Lie algebra.