|
gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:appearsIn
|
gptkb:McKay_correspondence
quiver representations
|
|
gptkbp:class
|
gptkb:ADE_classification
|
|
gptkbp:contrastsWith
|
gptkb:affine_Dynkin_diagrams
indefinite Dynkin diagrams
|
|
gptkbp:hasEdge
|
corresponds to angle between roots
|
|
gptkbp:hasEdgeMultiplicity
|
1 or 2 or 3
|
|
gptkbp:hasMaximalType
|
gptkb:E_8
|
|
gptkbp:hasNoCycles
|
true
|
|
gptkbp:hasProperty
|
connected
simply laced (for ADE types)
|
|
gptkbp:hasSmallestType
|
gptkb:A_1
|
|
gptkbp:hasSubgroup
|
gptkb:Dynkin_diagrams
|
|
gptkbp:hasType
|
gptkb:E_6
gptkb:E_7
gptkb:E_8
gptkb:G_2
F_4
A_n (n ≥ 1)
B_n (n ≥ 2)
C_n (n ≥ 3)
D_n (n ≥ 4)
|
|
gptkbp:hasVertex
|
corresponds to simple root
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
finite Dynkin diagrams
|
|
gptkbp:includes
|
gptkb:C_n
gptkb:E_6
gptkb:E_7
gptkb:E_8
gptkb:G_2
A_n
B_n
D_n
F_4
|
|
gptkbp:namedAfter
|
gptkb:Eugene_Dynkin
|
|
gptkbp:relatedTo
|
gptkb:Coxeter_groups
gptkb:Weyl_groups
gptkb:Cartan_matrices
gptkb:finite_reflection_groups
root systems
simple Lie algebras
|
|
gptkbp:usedFor
|
classifying root systems
classifying finite Coxeter groups
classifying semisimple Lie algebras
classifying simple Lie algebras
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
representation theory
singularity theory
Lie algebra classification
|
|
gptkbp:bfsParent
|
gptkb:affine_Dynkin_diagrams
gptkb:extended_Dynkin_diagrams
|
|
gptkbp:bfsLayer
|
8
|