In mathematics and physics, a "root system" refers to a specific structure that arises in the study of Lie algebras, algebraic groups, and other areas such as representation theory and geometry. A root system generally consists of: 1. **Set of Roots**: A root system is a finite set of vectors (called roots) in a Euclidean space that satisfy certain symmetric properties. Each root typically corresponds to some symmetry in a Lie algebra.
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A root system is a finite set of nonzero vectors closed under the reflections they define and satisfying the crystallographic integrality condition when it arises from a semisimple Lie algebra.