For a Lie algebra with bracket [·,·], [X,[Y,Z]] + [Y,[Z,X]] + [Z,[X,Y]] = 0 for all X, Y, Z. Replaces the associative law (which non-commutative brackets cannot satisfy) and expresses that ad_X = [X, −] is a derivation of the bracket.
For a Lie algebra with bracket [·,·], [X,[Y,Z]] + [Y,[Z,X]] + [Z,[X,Y]] = 0 for all X, Y, Z. Replaces the associative law (which non-commutative brackets cannot satisfy) and expresses that ad_X = [X, −] is a derivation of the bracket.