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gptkbp:instanceOf
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gptkb:mathematical_concept
|
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gptkbp:application
|
gptkb:geometry
gptkb:theoretical_physics
partial differential equations
quantum mechanics
|
|
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
gptkb:additive_group_of_real_numbers
gptkb:circle_group
orthogonal group
|
|
gptkbp:field
|
gptkb:mathematics
differential geometry
group theory
representation theory
|
|
gptkbp:hasInvariant
|
gptkb:fundamental_group
gptkb:Weyl_group
gptkb:center
gptkb:list
gptkb:fiber
gptkb:knowledge_representation
gptkb:Casimir_operator
gptkb:Killing_form
gptkb:Lie_group
gptkb:root
gptkb:Bruhat_decomposition
gptkb:Cartan_decomposition
gptkb:Cartan_subgroup
gptkb:Haar_measure
gptkb:Iwasawa_decomposition
gptkb:Plancherel_theorem
gptkb:characteristic_classes
gptkb:maximal_torus
gptkb:universal_covering_group
Fourier analysis
harmonic analysis
representation theory
homology
adjoint representation
exponential map
representation ring
structure constants
cohomology
principal bundle
dimension
flag manifold
homogeneous space
Borel subgroup
automorphism group
character table
coadjoint orbit
induced representation
inner automorphism group
irreducible representation
orbit method
outer automorphism group
polar decomposition
projective representation
symmetric space
unitary representation
weight lattice
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Lie groups
|
|
gptkbp:importantFor
|
gptkb:Peter–Weyl_theorem
gptkb:Lie's_third_theorem
gptkb:Baker–Campbell–Hausdorff_formula
gptkb:Cartan's_theorem
Lie correspondence
|
|
gptkbp:namedAfter
|
gptkb:Sophus_Lie
|
|
gptkbp:property
|
group operations are smooth maps
|
|
gptkbp:relatedConcept
|
gptkb:group_of_people
gptkb:topology
gptkb:Lie_group
|
|
gptkbp:structure
|
gptkb:group_of_people
gptkb:Riemannian_manifold
|
|
gptkbp:studiedBy
|
gptkb:Sophus_Lie
gptkb:algebraic_geometry
gptkb:topology
differential geometry
representation theory
|
|
gptkbp:studiedIn
|
19th century
|
|
gptkbp:subunit
|
gptkb:Lie_group
Lie subgroup
homogeneous space
|
|
gptkbp:bfsParent
|
gptkb:Gregory_Margulis
gptkb:Grigory_Margulis
|
|
gptkbp:bfsLayer
|
4
|