Lie algebras

A Lie algebra is a mathematical structure that studies how certain elements, called generators, interact through a special operation known as the Lie bracket. This operation captures the concept of "commutation," or how two elements relate when combined in different orders, which often reveals underlying symmetries or geometric properties. Lie algebras are fundamental in understanding continuous symmetry in physics and mathematics, such as rotations and conserved quantities, by providing an algebraic framework to analyze smooth changes and transformations within systems.