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gptkbp:instanceOf
|
Lie algebra type
|
|
gptkbp:allows
|
n ≥ 4
|
|
gptkbp:alsoKnownAs
|
D_n
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|
gptkbp:automorphismGroup
|
gptkb:diagram_automorphism_(for_n_≥_4)
|
|
gptkbp:Cartan_matrix
|
gptkb:D_n_Cartan_matrix
|
|
gptkbp:centralTo
|
Z_2 (for n odd)
Z_2 × Z_2 (for n even)
Z_4 (for n even)
Z_4 (for n odd)
|
|
gptkbp:class
|
gptkb:Lie_group
gptkb:classical_Lie_algebra
|
|
gptkbp:dimensions
|
n(2n-1)
|
|
gptkbp:Dynkin_diagram
|
gptkb:D_n_diagram
|
|
gptkbp:field
|
complex numbers
real numbers
|
|
gptkbp:firstAppearance
|
gptkb:Cartan_classification
|
|
gptkbp:fundamentalGroup
|
Z_2 × Z_2 (for n even)
Z_4 (for n odd)
|
|
gptkbp:hasSpecialCase
|
D_2 is isomorphic to A_1 × A_1
D_3 is isomorphic to A_3
D_4 is triality Lie algebra
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Lie type D n
|
|
gptkbp:rank
|
n
|
|
gptkbp:relatedGroup
|
gptkb:SO(2n)
gptkb:Spin(2n)
|
|
gptkbp:relatedTo
|
gptkb:Lie_type_C_n
gptkb:exceptional_Lie_algebras
gptkb:Lie_type_A_n
gptkb:Lie_type_B_n
gptkb:orthogonal_Lie_algebras
gptkb:root_lattice_D_n
gptkb:triality_(for_D_4)
gptkb:Clifford_algebras
orthogonal group
spin representations
|
|
gptkbp:subclassOf
|
gptkb:Lie_algebra_of_type_B_n+1
|
|
gptkbp:type
|
gptkb:D_n_root_system
|
|
gptkbp:usedIn
|
gptkb:geometry
gptkb:theoretical_physics
gptkb:string_theory
coding theory
crystallography
representation theory
algebraic groups
lattice theory
grand unified theories
|
|
gptkbp:Weyl_group
|
gptkb:even_signed_permutation_group
|
|
gptkbp:bfsParent
|
gptkb:special_orthogonal_group_SO(n,q)
|
|
gptkbp:bfsLayer
|
7
|