|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:adjointRepresentationDimension
|
24
|
|
gptkbp:automorphismGroup
|
PGL(5)
|
|
gptkbp:basisFor
|
traceless 5x5 matrices
|
|
gptkbp:CartanSubalgebraDimension
|
4
|
|
gptkbp:centralTo
|
trivial
|
|
gptkbp:complexForm
|
sl(5, C)
|
|
gptkbp:dimensions
|
24
|
|
gptkbp:Dynkin_diagram
|
gptkb:A4
|
|
gptkbp:field
|
arbitrary field (with char ≠ 5)
|
|
gptkbp:fullName
|
special linear Lie algebra of 5x5 matrices
|
|
gptkbp:highestWeightRepresentation
|
fundamental representations correspond to partitions of 5
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Lie algebra sl(5)
|
|
gptkbp:KillingForm
|
non-degenerate
|
|
gptkbp:notation
|
sl(5, C)
sl(5, R)
|
|
gptkbp:rank
|
4
complex numbers
real numbers
|
|
gptkbp:realForm
|
sl(5, R)
|
|
gptkbp:relatedGroup
|
SL(5)
|
|
gptkbp:structureConstants
|
given by commutator of matrices
|
|
gptkbp:subalgebra
|
sl(2)
sl(3)
sl(4)
|
|
gptkbp:type
|
gptkb:A4
gptkb:Lie_group
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:theoretical_physics
representation theory
|
|
gptkbp:Weyl_group
|
gptkb:symmetric_group_S5
|
|
gptkbp:bfsParent
|
gptkb:A4_(Dynkin_type)
|
|
gptkbp:bfsLayer
|
7
|