Hopf algebra

例句：

1. 1. In the studyof quantum mechanics, Hopfalgebra plays a crucial role in modeling the behavior of quantum systems.
   在量子力学研究中，霍普夫代数在模拟量子系统行为中扮演着至关重要的角色。
2. 2. The Hopf algebra isused to describe the dynamics of chemical reactions.
   霍普夫代数被用来描述化学反应的动态过程。
3. 3. The Hopf algebra has been applied to various fields suchas cryptography and neural networks.
   霍普夫代数已经被应用到密码学和神经网络等多个领域。