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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:actsOn
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gptkb:Euclidean_space
gptkb:Vector_spaces
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gptkbp:application
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gptkb:Algebraic_geometry
gptkb:Crystallography
Combinatorics
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gptkbp:class
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Complex reflection groups classified by Shephard and Todd
Finite real reflection groups classified by Coxeter diagrams
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gptkbp:definedIn
|
Groups generated by reflections
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gptkbp:finiteClassification
|
Classified by Coxeter
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gptkbp:finiteOrInfinite
|
Can be finite or infinite
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gptkbp:finiteTypes
|
A_n, B_n, D_n, E_6, E_7, E_8, F_4, H_3, H_4, I_2(n)
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gptkbp:hasProperty
|
Defined by relations of order 2 and products
Generated by involutions
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|
https://www.w3.org/2000/01/rdf-schema#label
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Reflection groups
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gptkbp:infiniteTypes
|
Affine Weyl groups
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gptkbp:notableExample
|
gptkb:Weyl_group
gptkb:Dihedral_group
gptkb:Symmetric_group
|
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gptkbp:notation
|
gptkb:Coxeter_notation
|
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gptkbp:relatedTo
|
gptkb:Coxeter_groups
gptkb:Lie_algebras
gptkb:Regular_polytopes
gptkb:Algebraic_groups
gptkb:Coxeter–Dynkin_diagram
gptkb:Dynkin_diagrams
Tessellations
Geometric group theory
Braid groups
Crystallographic groups
Hyperplane arrangements
Invariant theory
Reflection representation
Root lattices
Root systems
Shephard–Todd classification
Symmetry groups
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|
gptkbp:studiedBy
|
gptkb:Ludwig_Schläfli
gptkb:H.S.M._Coxeter
|
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gptkbp:studiedIn
|
gptkb:Lie_theory
gptkb:geometry
gptkb:Group_theory
|
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gptkbp:subclassOf
|
gptkb:Weyl_group
gptkb:group_of_people
|
|
gptkbp:usedIn
|
Theory of tessellations
Theory of Lie groups
Theory of regular polytopes
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|
gptkbp:bfsParent
|
gptkb:Reflection_Groups_and_Coxeter_Groups
|
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gptkbp:bfsLayer
|
7
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