|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:adjointRepresentation
|
3-dimensional
|
|
gptkbp:appearsIn
|
gptkb:theory_of_special_relativity
gptkb:algebraic_geometry
modular forms
partial differential equations
Lorentz group representation
quantum angular momentum
|
|
gptkbp:automorphismGroup
|
gptkb:PGL(2,C)
|
|
gptkbp:basisFor
|
{E, F, H}
|
|
gptkbp:CartanSubalgebraDimension
|
1
|
|
gptkbp:CasimirElement
|
exists
|
|
gptkbp:centralTo
|
{0}
|
|
gptkbp:commutatorSubalgebra
|
gptkb:sl(2,C)
|
|
gptkbp:complexification
|
gptkb:su(2)
gptkb:sl(2,R)
|
|
gptkbp:definesProperty
|
trace zero 2x2 complex matrices
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:field
|
complex numbers
|
|
gptkbp:finiteDimensionalIrreducibleRepresentations
|
classified by highest weight
|
|
gptkbp:fullName
|
special linear Lie algebra of 2x2 complex matrices
|
|
gptkbp:highestWeightTheory
|
applies
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
sl(2,C)
|
|
gptkbp:isomorphicTo
|
so(3,C)
sp(2,C)
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:KillingForm
|
non-degenerate
|
|
gptkbp:notation
|
gptkb:sl(2,C)
|
|
gptkbp:rank
|
1
|
|
gptkbp:realForm
|
gptkb:su(2)
gptkb:sl(2,R)
|
|
gptkbp:relatedGroup
|
gptkb:SL(2,C)
|
|
gptkbp:structureConstants
|
[H,E]=2E, [H,F]=-2F, [E,F]=H
|
|
gptkbp:type
|
A1
|
|
gptkbp:universalEnvelopingAlgebra
|
U(sl(2,C))
|
|
gptkbp:usedIn
|
gptkb:quantum_field_theory
gptkb:theoretical_physics
differential geometry
quantum mechanics
representation theory
|
|
gptkbp:Weyl_group
|
gptkb:Z/2Z
|
|
gptkbp:bfsParent
|
gptkb:SL(2,C)
gptkb:Lie_algebra_su(2)
gptkb:SU(2)_algebra
gptkb:su(2)
|
|
gptkbp:bfsLayer
|
7
|