Lie Theory

Lie Theory, named after mathematician Sophus Lie, is a branch of mathematics that studies symmetries and transformations using structures called Lie groups and Lie algebras. In simple terms, it explores how objects change while preserving certain properties, like rotating or reflecting shapes without altering their form. These concepts are fundamental in various fields, including physics, where they help describe symmetries in physical laws, and in mathematics, where they inform geometry and differential equations. Essentially, Lie Theory connects algebraic structures with geometric ideas, providing a framework to understand continuous symmetries in both mathematics and science.