root systems

Root systems refer to a mathematical framework used in algebra and geometry, particularly in the study of symmetry and group theory. They consist of a set of vectors (roots) that describe how certain algebraic objects, like Lie algebras, behave under symmetries. Each root corresponds to a direction in space, and relationships between these roots reveal essential properties of the system. Root systems help classify geometrical shapes and mathematical structures, making them fundamental in various fields, including physics, particularly in understanding particle physics and string theory.