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gptkbp:instanceOf
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gptkb:group_of_people
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gptkbp:application
|
gptkb:algebraic_geometry
gptkb:Lie_groups
crystallography
combinatorics
classification of regular polytopes
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gptkbp:characterizedBy
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gptkb:Weyl_group
gptkb:Coxeter_matrix
|
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gptkbp:class
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gptkb:indefinite_Coxeter_groups
gptkb:affine_Coxeter_groups
gptkb:finite_Coxeter_groups
gptkb:hyperbolic_Coxeter_groups
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|
gptkbp:defines
|
group generated by reflections subject to relations of order two and certain products
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|
gptkbp:example
|
gptkb:Weyl_groups
gptkb:affine_Weyl_groups
gptkb:group_of_people
gptkb:finite_reflection_groups
dihedral group
|
|
gptkbp:field
|
gptkb:algebra
gptkb:geometry
gptkb:mathematics
group theory
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gptkbp:hasSubgroup
|
gptkb:Weyl_group
gptkb:group_of_people
dihedral group
hyperoctahedral group
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|
https://www.w3.org/2000/01/rdf-schema#label
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Coxeter groups
|
|
gptkbp:introducedIn
|
1930s
|
|
gptkbp:namedAfter
|
gptkb:H._S._M._Coxeter
|
|
gptkbp:notableMember
|
gptkb:A_n_(symmetric_group)
gptkb:B_n_(hyperoctahedral_group)
gptkb:I_2(n)_(dihedral_group)
gptkb:E_6
gptkb:E_7
gptkb:E_8
gptkb:H_4
D_n
F_4
H_3
|
|
gptkbp:presentedBy
|
Coxeter presentation
|
|
gptkbp:property
|
can be finite or infinite
generated by involutions
presentation by generators and relations
|
|
gptkbp:relatedTo
|
gptkb:Euclidean_geometry
gptkb:hyperbolic_geometry
gptkb:spherical_geometry
gptkb:Dynkin_diagrams
root systems
reflection groups
|
|
gptkbp:studiedBy
|
gptkb:Wilhelm_Killing
gptkb:Élie_Cartan
gptkb:H._S._M._Coxeter
|
|
gptkbp:usedIn
|
representation theory
algebraic combinatorics
theory of buildings
|
|
gptkbp:bfsParent
|
gptkb:Coxeter–Dynkin_diagrams
gptkb:Hecke_algebra
|
|
gptkbp:bfsLayer
|
6
|