In mathematics, in particular the theory of Lie algebras, the Weyl group of a root system Φ 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.
It is named after Hermann Weyl.
Read more about Weyl Group: Examples, Weyl Chambers, Coxeter Group Structure, Definition, Bruhat Decomposition, Analogy With Algebraic Groups, Cohomology
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