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gptkbp:instanceOf
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gptkb:mathematical_concept
|
|
gptkbp:application
|
differential geometry
particle physics
representation theory
|
|
gptkbp:characterizedBy
|
no nontrivial connected normal subgroups
|
|
gptkbp:class
|
gptkb:Cartan_classification
gptkb:Dynkin_diagrams
A_n, B_n, C_n, D_n, E_6, E_7, E_8, F_4, G_2 types
|
|
gptkbp:finiteCover
|
simply connected simple Lie group
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
simple Lie groups
|
|
gptkbp:includes
|
gptkb:exceptional_Lie_groups
gptkb:special_orthogonal_group_SO(n)
gptkb:symplectic_group_Sp(n)
gptkb:special_linear_group_SL(n,R)
|
|
gptkbp:namedAfter
|
gptkb:Sophus_Lie
|
|
gptkbp:property
|
connected
non-abelian (except for one-dimensional case)
|
|
gptkbp:relatedTo
|
gptkb:Lie_algebras
gptkb:semisimple_Lie_groups
|
|
gptkbp:studiedIn
|
gptkb:mathematics
gptkb:theoretical_physics
|
|
gptkbp:subclassOf
|
gptkb:Lie_group
simple group
|
|
gptkbp:usedIn
|
gptkb:gauge_theory
gptkb:Standard_Model_of_particle_physics
|
|
gptkbp:bfsParent
|
gptkb:Lie_group
gptkb:Lie_groups
|
|
gptkbp:bfsLayer
|
5
|