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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 at least one of the roots, and as such is a finite reflection group. In…

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Weyl groups in algebraic, group-theoretic, and geometric settings

Lie groupSymmetric spaceCartan subalgebraWeyl groupWeights
13 related topics

Bruhat decomposition

Borel subgroupConnectedSolvableBruhat decompositionFlag variety
8 related topics

Coxeter group structure

Dynkin diagramCoxeter–Dynkin diagramPresentationBruhat orderLength function
7 related topics

Overview

MathematicsLie algebraHermann WeylRoot systemSubgroup
13 related topics

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Overview

Coxeter group structure

Weyl groups in algebraic, group-theoretic, and geometric settings

Bruhat decomposition

Analogy with algebraic groups

Cohomology

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Weyl group

Nodes54
Edges53
Triples56
Avg. degree1.96
Density0.037037
Components1

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Weyl group

Top relations

related to Cohomology · 9
Weyl group → Dynkin, For, Hämmerli, Lie, Matthey, Out, Suter, The, Weyl
related to As a Coxeter group · 8
Weyl group → Being, Bruhat, Coxeter, Dynkin, The, There, We, Weyl
related to Weyl chambers · 8
Weyl group → Delta, If, Phi, Recall, Since, The, Thus, Weyl
related to Definition and examples · 6
Weyl group → By, Euclidean, For, Let, Phi, The Weyl
related to In other settings · 6
Weyl group → Cartan, For, Lie, NG, Weyl, ZG
related to Weyl groups in algebraic, group-theoretic, and geometric settings · 6
Weyl group → Above, Cartan, For, Lie, There, Weyl
related to Generating set · 4
Weyl group → Delta, Phi, That, Weyl
is a · 3
Weyl group → group of transformations of V, symmetric group, symmetry group of an equilateral triangle
related to Analogy with algebraic groups · 3
Weyl group → There, This, Weyl
see also · 3
Weyl group → Affine Weyl, Cartan, Lie

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Important terminology

group weyl displaystyle root alpha system torus lie groups phi roots finite coxeter maximal subgroup reflections one reflection algebra connected

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Weyl groupis asymmetry group of an equilateral triangle0.90text
Weyl groupis agroup of transformations of V0.90text
Weyl groupis asymmetric group0.90text
Weyl grouprelated to Analogy with algebraic groupsThere0.60section
Weyl grouprelated to Analogy with algebraic groupsWeyl0.60section
Weyl grouprelated to Analogy with algebraic groupsThis0.60section
Weyl grouprelated to As a Coxeter groupWeyl0.60section
Weyl grouprelated to As a Coxeter groupCoxeter0.60section
Weyl grouprelated to As a Coxeter groupDynkin0.60section
Weyl grouprelated to As a Coxeter groupBeing0.60section
Weyl grouprelated to As a Coxeter groupThe0.60section
Weyl grouprelated to As a Coxeter groupWe0.60section

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    Min side: 3
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