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- Lie–Palais_theorem abstract "In differential geometry, the Lie–Palais theorem states that an action of a finite-dimensional Lie algebra on a smooth compact manifold can be lifted to an action of a finite-dimensional Lie group. For manifolds with boundary the action must preserve the boundary, in other words the vector fields on the boundary must be tangent to the boundary. Palais (1957) proved it as a global form of an earlier local theorem due to Sophus Lie.The example of the vector field d/dx on the open unit interval shows that the result is false for non-compact manifolds.Without the assumption that the Lie algebra is finite dimensional the result can be false. Milnor (1984, p. 1048) gives the following example due to Omori: the Lie algebra is all vector fields f(x,y)∂/∂x + g(x,y)∂/∂y acting on the torus R2/Z2 such that g(x, y) = 0 for 0 ≤ x ≤ 1/2. This Lie algebra is not the Lie algebra of any group. Pestov (1995) gives an infinite dimensional generalization of the Lie–Palais theorem for Banach–Lie algebras with finite-dimensional center.".
- Lie–Palais_theorem wikiPageExternalLink 9403004.
- Lie–Palais_theorem wikiPageID "37647580".
- Lie–Palais_theorem wikiPageLength "2289".
- Lie–Palais_theorem wikiPageOutDegree "11".
- Lie–Palais_theorem wikiPageRevisionID "650829948".
- Lie–Palais_theorem wikiPageWikiLink Category:Lie_algebras.
- Lie–Palais_theorem wikiPageWikiLink Category:Theorems_in_differential_geometry.
- Lie–Palais_theorem wikiPageWikiLink Closed_manifold.
- Lie–Palais_theorem wikiPageWikiLink Differentiable_manifold.
- Lie–Palais_theorem wikiPageWikiLink Differential_geometry.
- Lie–Palais_theorem wikiPageWikiLink Group_action.
- Lie–Palais_theorem wikiPageWikiLink Lie_algebra.
- Lie–Palais_theorem wikiPageWikiLink Lie_group.
- Lie–Palais_theorem wikiPageWikiLink Sophus_Lie.
- Lie–Palais_theorem wikiPageWikiLink Unit_interval.
- Lie–Palais_theorem wikiPageWikiLink Vector_field.
- Lie–Palais_theorem wikiPageWikiLinkText "Lie–Palais theorem".
- Lie–Palais_theorem wikiPageUsesTemplate Template:Citation.
- Lie–Palais_theorem wikiPageUsesTemplate Template:Harvs.
- Lie–Palais_theorem wikiPageUsesTemplate Template:Harvtxt.
- Lie–Palais_theorem subject Category:Lie_algebras.
- Lie–Palais_theorem subject Category:Theorems_in_differential_geometry.
- Lie–Palais_theorem type Algebra.
- Lie–Palais_theorem type Physic.
- Lie–Palais_theorem type Theorem.
- Lie–Palais_theorem comment "In differential geometry, the Lie–Palais theorem states that an action of a finite-dimensional Lie algebra on a smooth compact manifold can be lifted to an action of a finite-dimensional Lie group. For manifolds with boundary the action must preserve the boundary, in other words the vector fields on the boundary must be tangent to the boundary.".
- Lie–Palais_theorem label "Lie–Palais theorem".
- Lie–Palais_theorem sameAs Q6544508.
- Lie–Palais_theorem sameAs m.0ndjkdw.
- Lie–Palais_theorem sameAs Q6544508.
- Lie–Palais_theorem wasDerivedFrom Lie–Palais_theorem?oldid=650829948.
- Lie–Palais_theorem isPrimaryTopicOf Lie–Palais_theorem.