A root system is a specific arrangement of vectors in a Euclidean space that arises in the study of Lie algebras and Lie groups. These vectors, known as roots, are associated with the structure of the algebra and provide crucial insights into its representation theory and symmetry properties. The roots are typically organized into a set that reflects the algebra's underlying symmetries, leading to the classification of simple Lie algebras and their representations.
congrats on reading the definition of root system. now let's actually learn it.