雅可比恒等式就是下列等式：

[X,[Y,Z]]+[Y,[Z,X]]+[Z,[X,Y]]=0

集合 有一个二元运算子及可交换二元运算子满足雅可比恒等式，如果

李代数是满足雅可比恒等式的代数结构的一个主要例子。

注意，满足雅可比恒等式的代数结构不一定满足反交换律。

In mathematics the Jacobi identity is a property a binary operation can have that determines how the order of evaluation behaves for the given operation. In contrast to plain associative operations, the order of evaluation is significant for operations satisfying the Jacobi identity. It is named after the German mathematician Carl Gustav Jakob Jacobi. The cross product and the bracket operation of a Lie algebra both satisfy the Jacobi identity.