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gptkbp:instanceOf
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gptkb:mathematical_concept
gptkb:topology
group theory concept
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gptkbp:application
|
partial differential equations
particle physics
representation theory
symmetry in physics
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gptkbp:class
|
classified by Élie Cartan
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gptkbp:defines
|
A Lie group is a group that is also a smooth manifold, where the group operations are smooth.
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gptkbp:example
|
gptkb:general_linear_group
gptkb:butter
gptkb:Heisenberg_group
gptkb:rotation_group
orthogonal group
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gptkbp:field
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gptkb:mathematics
|
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gptkbp:firstDescribed
|
19th century
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gptkbp:hasConcept
|
gptkb:semisimple_Lie_group
gptkb:Lie_group
gptkb:matrix_Lie_group
gptkb:Abelian_Lie_group
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gptkbp:hasSubfield
|
gptkb:algebra
gptkb:theoretical_physics
differential geometry
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|
https://www.w3.org/2000/01/rdf-schema#label
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Groupes de Lie
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gptkbp:languageOfOrigin
|
gptkb:French
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gptkbp:namedAfter
|
gptkb:Sophus_Lie
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gptkbp:property
|
can be compact or non-compact
locally Euclidean
connected or disconnected
finite-dimensional or infinite-dimensional
smooth group operations
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gptkbp:relatedTo
|
gptkb:topology
gptkb:Riemannian_manifold
gptkb:Lie_group
representation theory
Lie bracket
exponential map
homogeneous space
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|
gptkbp:studiedBy
|
gptkb:Sophus_Lie
gptkb:Wilhelm_Killing
gptkb:Élie_Cartan
|
|
gptkbp:bfsParent
|
gptkb:Groupes_algébriques
|
|
gptkbp:bfsLayer
|
7
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