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In mathematics, a Lie group (pronounced /liː/ Lee) is a group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
History, Definitions and examples & More examples of Lie groups
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lie group groups displaystyle algebra connected subgroup theory example one manifold mathbb matrices real map simple space algebras smooth representations
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Lie group | is a | group that is also a finite-dimensional real smooth manifold | 0.90 | text |
| Lie group | is a | group object in the category of smooth manifolds | 0.90 | text |
| Lie group | is a | Lie group | 0.90 | text |
| Lie group | is a | Lie algebra under the Lie bracket of vector fields.Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tan… | 0.90 | text |
| Lie group | is a | semidirect product of a solvable normal subgroup and a semisimple subgroup.Connected compact Lie groups are all known | 0.90 | text |
| Lie group | is a | open normal subgroup | 0.90 | text |
| Lie group | is a | simply connected Lie group | 0.90 | text |
| Lie group | is a | example of a gauge group | 0.90 | text |
| Lie group | related to Additional examples | The | 0.60 | section |
| Lie group | related to Additional examples | SU | 0.60 | section |
| Lie group | related to Additional examples | Topologically | 0.60 | section |
| Lie group | related to Additional examples | The Heisenberg | 0.60 | section |
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