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gptkbp:instanceOf
|
gptkb:mathematical_concept
|
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gptkbp:application
|
partial differential equations
particle physics
quantum mechanics
symmetry analysis
|
|
gptkbp:category
|
gptkb:topology
gptkb:Riemannian_manifold
|
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gptkbp:class
|
gptkb:compact_Lie_groups
gptkb:Abelian_Lie_groups
gptkb:connected_Lie_groups
gptkb:nilpotent_Lie_groups
gptkb:semisimple_Lie_groups
gptkb:simple_Lie_groups
gptkb:solvable_Lie_groups
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|
gptkbp:defines
|
group that is also a smooth manifold
|
|
gptkbp:example
|
gptkb:general_linear_group
gptkb:rotation_group
orthogonal group
|
|
gptkbp:field
|
gptkb:mathematics
gptkb:theoretical_physics
differential geometry
group theory
|
|
gptkbp:hasAssociatedObject
|
gptkb:Lie_group
adjoint representation
exponential map
|
|
gptkbp:hasInvariant
|
gptkb:Haar_measure
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Lie Groups
|
|
gptkbp:namedAfter
|
gptkb:Sophus_Lie
|
|
gptkbp:originatedIn
|
gptkb:Sophus_Lie
|
|
gptkbp:property
|
group operations are smooth
|
|
gptkbp:relatedConcept
|
gptkb:Lie_group
Lie subgroup
homogeneous space
|
|
gptkbp:structure
|
group structure
differentiable structure
|
|
gptkbp:studiedBy
|
19th century
|
|
gptkbp:studiedIn
|
gptkb:topology
harmonic analysis
representation theory
|
|
gptkbp:theory
|
gptkb:Peter–Weyl_theorem
gptkb:Lie's_third_theorem
gptkb:Baker–Campbell–Hausdorff_formula
gptkb:Cartan's_theorem
|
|
gptkbp:usedIn
|
gptkb:gauge_theory
gptkb:string_theory
control theory
crystallography
|
|
gptkbp:bfsParent
|
gptkb:Daniel_Bump
|
|
gptkbp:bfsLayer
|
6
|