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algebra > group theory > topological group > Lie group > Weyl group

algebra > differential algebra > Lie algebra > Weyl group

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Weyl group

In mathematics, in particular the theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system Φ is a subgroup of the isometry group of that 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. In fact it turns out that most finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Weyl_group)

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