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
Famous quotes containing the word group:
“The poet who speaks out of the deepest instincts of man will be heard. The poet who creates a myth beyond the power of man to realize is gagged at the peril of the group that binds him. He is the true revolutionary: he builds a new world.”
—Babette Deutsch (1895–1982)