令 是一个加法群, “*” 是定义在 上的二元运算。
如果“*”满足以下条件：
对于任意的 ，有，
那幺，我们说二元运算“*”满足反交换律。

• 减法
• 外积
• 李代数

In mathematics, anticommutativity is the property of an operation with two or more arguments wherein swapping the position of any two arguments negates the result. Anticommutative operations are widely used in algebra, geometry, mathematical analysis and, as a consequence, in physics: they are often called antisymmetric operations.