special orthogonal Lie algebra

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Lie_group
gptkbp:alsoKnownAs	so(n)
gptkbp:appearsIn	gptkb:theoretical_physics differential geometry representation theory
gptkbp:associatedWith	gptkb: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
gptkbp:Lie_bracket	matrix commutator
gptkbp:notation	so(n, F)
gptkbp:rank	complex numbers real numbers
gptkbp:relatedTo	gptkb:Lie_group gptkb:orthogonal_group gptkb:orthogonal_Lie_algebra gptkb:special_linear_Lie_algebra
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
https://www.w3.org/2000/01/rdf-schema#label	special orthogonal Lie algebra