Lie Group

A Lie group is a mathematical structure that combines geometric shapes with symmetry. Specifically, it’s a group that is also a smooth, continuous shape (like a sphere or doughnut), allowing us to smoothly move or transform objects within it without breaking its structure. These groups are used to describe continuous symmetries in physical systems, such as rotations and vibrations, and are fundamental in areas like physics and geometry. Essentially, a Lie group helps us understand how objects can be smoothly and systematically transformed while maintaining their essential properties.