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- Lie_algebra_bundle abstract "In Mathematics, a weak Lie algebra bundleis a vector bundle over a base space X together with a morphismwhich induces a Lie algebra structure on each fibre .A Lie algebra bundle is a vector bundle in whicheach fibre is a Lie algebra and for every x in X, there is an open set containing x, a Lie algebra L and a homeomorphismsuch thatis a Lie algebra isomorphism.Any Lie algebra bundle is a weak Lie algebra bundle but the converse need not be true in general.As an example of a weak Lie algebra bundle that is not a strong Lie algebra bundle, consider the total space over the real line . Let [.,.] denote the Lie bracket of and deform it by the real parameter as:for and .Lie's third theorem states that every bundle of Lie algebras can locally be integrated to a bundle of Lie groups. However globally the total space might fail to be Hausdorff.".
- Lie_algebra_bundle wikiPageID "11269476".
- Lie_algebra_bundle wikiPageRevisionID "592546150".
- Lie_algebra_bundle hasPhotoCollection Lie_algebra_bundle.
- Lie_algebra_bundle subject Category:Algebraic_topology.
- Lie_algebra_bundle subject Category:Complex_analysis.
- Lie_algebra_bundle subject Category:Differential_topology.
- Lie_algebra_bundle subject Category:Vector_bundles.
- Lie_algebra_bundle type Abstraction100002137.
- Lie_algebra_bundle type Collection107951464.
- Lie_algebra_bundle type Group100031264.
- Lie_algebra_bundle type Package108008017.
- Lie_algebra_bundle type VectorBundles.
- Lie_algebra_bundle comment "In Mathematics, a weak Lie algebra bundleis a vector bundle over a base space X together with a morphismwhich induces a Lie algebra structure on each fibre .A Lie algebra bundle is a vector bundle in whicheach fibre is a Lie algebra and for every x in X, there is an open set containing x, a Lie algebra L and a homeomorphismsuch thatis a Lie algebra isomorphism.Any Lie algebra bundle is a weak Lie algebra bundle but the converse need not be true in general.As an example of a weak Lie algebra bundle that is not a strong Lie algebra bundle, consider the total space over the real line . ".
- Lie_algebra_bundle label "Lie algebra bundle".
- Lie_algebra_bundle sameAs m.02r5qqj.
- Lie_algebra_bundle sameAs Q6543805.
- Lie_algebra_bundle sameAs Q6543805.
- Lie_algebra_bundle sameAs Lie_algebra_bundle.
- Lie_algebra_bundle wasDerivedFrom Lie_algebra_bundle?oldid=592546150.
- Lie_algebra_bundle isPrimaryTopicOf Lie_algebra_bundle.