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gptkbp:instanceOf
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gptkb:Lie_group
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gptkbp:alsoKnownAs
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so(2n)
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gptkbp:appearsIn
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gptkb:string_theory
gptkb:Grand_Unified_Theories
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gptkbp:automorphismGroup
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outer automorphism (for n ≥ 4)
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gptkbp:Cartan_matrix
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D
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gptkbp:centralTo
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Z_2 × Z_2 (for n even)
Z_4 (for n odd)
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gptkbp:class
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one of four infinite families of simple Lie algebras
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gptkbp:complexification
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so(2n,ℝ)
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gptkbp:definedIn
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skew-symmetric matrices of size 2n×2n with trace zero
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gptkbp:dimensions
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n(2n-1)
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gptkbp:Dynkin_diagram
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D_n
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gptkbp:field
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ℂ
ℝ
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gptkbp:hasFundamentalRepresentation
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spinor representation
vector representation
conjugate spinor representation
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gptkbp:hasRootLength
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all roots have the same length
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gptkbp:hasSpecialProperty
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gptkb:triality_(for_D_4)
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https://www.w3.org/2000/01/rdf-schema#label
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D n Lie algebra
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gptkbp:lowestNontrivialCase
|
D_3 ≅ A_3
D_4 (triality)
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gptkbp:rank
|
n
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gptkbp:realForm
|
so(2n,0)
so(n,n)
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gptkbp:relatedGroup
|
gptkb:SO(2n)
gptkb:Spin(2n)
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gptkbp:relatedLieAlgebra
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gptkb:E_6_Lie_algebra
gptkb:E_7_Lie_algebra
gptkb:G_2_Lie_algebra
gptkb:E_8_Lie_algebra
gptkb:A_n_Lie_algebra
gptkb:F_4_Lie_algebra
B_n Lie algebra
C_n Lie algebra
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gptkbp:relatedTo
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gptkb:Lie_group
gptkb:special_orthogonal_Lie_algebra
orthogonal group
|
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gptkbp:type
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gptkb:Lie_group
gptkb:classical_Lie_algebra
gptkb:D_n_root_system
|
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gptkbp:usedIn
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gptkb:theoretical_physics
differential geometry
representation theory
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gptkbp:Weyl_group
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gptkb:Weyl_group_of_type_D_n
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gptkbp:bfsParent
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gptkb:D_n_root_lattice
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gptkbp:bfsLayer
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6
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