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