In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras. Since Lie groups (and some analogues such as algebraic groups) and Lie algebras have become important in many parts of mathematics during the twentieth century, the apparently special nature of root systems belies the number of areas in which they are applied. Further, the classification scheme for root systems, by Dynkin diagrams, occurs in parts of mathematics with no overt connection to Lie theory (such as singularity theory). Finally, root systems are important for their own sake, as in graph theory in the study of eigenvalues.
Read more about Root System: Definitions and First Examples, History, Elementary Consequences of The Root System Axioms, Positive Roots and Simple Roots, Dual Root System and Coroots, Classification of Root Systems By Dynkin Diagrams, Properties of The Irreducible Root Systems, Root Systems and Lie Theory
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