Weyl Groups

Weyl groups are mathematical tools that describe symmetries within certain complex structures called Lie algebras, which are foundational in understanding symmetries in physics and geometry. Imagine a crystal lattice where parts can be rotated or reflected without changing its overall appearance; Weyl groups similarly encapsulate all possible symmetries of a system's fundamental building blocks. They help classify and analyze these symmetries systematically, enabling mathematicians and physicists to understand how complex symmetrical objects are organized and how they behave under various transformations.