Weyl Group
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High Quality Content by WIKIPEDIA articles! In mathematics, in particular the theory of Lie algebras, the Weyl group of a root system is a subgroup of the isometry group of the root system. Specifically, it is the subgroup which is generated by reflections through the hyperplanes orthogonal to the roots, and as such is a finite reflection group. Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these. The Weyl group of a semi-simple Lie group, a semi-simple Lie algebra, a semi-simple linear algebraic group, etc. is the Weyl group of the root system of that group or algebra.…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, in particular the theory of Lie algebras, the Weyl group of a root system is a subgroup of the isometry group of the root system. Specifically, it is the subgroup which is generated by reflections through the hyperplanes orthogonal to the roots, and as such is a finite reflection group. Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these. The Weyl group of a semi-simple Lie group, a semi-simple Lie algebra, a semi-simple linear algebraic group, etc. is the Weyl group of the root system of that group or algebra.