Lie groups

Lie groups are mathematical structures that combine concepts from algebra and geometry. They are named after the Norwegian mathematician Sophus Lie, who studied them in the context of continuous transformation groups. ### Basic Definition A **Lie group** is a group that is also a smooth manifold, meaning that the group operations (multiplication and inversion) are smooth (infinitely differentiable) functions. This combination allows for the study of algebraic structures (like groups) with the tools of calculus and differential geometry.