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special orthogonal Lie algebra
URI:
https://gptkb.org/entity/special_orthogonal_Lie_algebra
GPTKB entity
Statements (31)
Predicate
Object
gptkbp:instanceOf
gptkb:Lie_group
gptkbp:alsoKnownAs
so(n)
gptkbp:appearsIn
gptkb:theoretical_physics
differential geometry
representation theory
gptkbp:associatedWith
orthogonal group
gptkbp:basisFor
skew-symmetric matrices
gptkbp:Cartan_type
B (for odd n), D (for even n)
gptkbp:centralTo
trivial for n odd, Z/2Z for n even
gptkbp:dimensions
n(n-1)/2
gptkbp:field
gptkb:Lie_theory
gptkb:algebra
gptkb:mathematics
gptkbp:generation
rotations in n-dimensional space
https://www.w3.org/2000/01/rdf-schema#label
special orthogonal Lie algebra
gptkbp:Lie_bracket
matrix commutator
gptkbp:notation
so(n, F)
gptkbp:rank
complex numbers
real numbers
gptkbp:relatedTo
gptkb:Lie_group
gptkb:orthogonal_Lie_algebra
gptkb:special_linear_Lie_algebra
orthogonal group
gptkbp:structure
simple Lie algebra (for n > 2)
gptkbp:subclassOf
gptkb:general_linear_Lie_algebra
gptkbp:type
B_n or D_n
gptkbp:usedIn
gptkb:gauge_theory
particle physics
quantum mechanics
gptkbp:bfsParent
gptkb:Lie_algebras
gptkbp:bfsLayer
6