An overview of Lie groups
Alphabetical list of Lie groups
Group | Manifold | $โ$ | Comment |
---|---|---|---|
GeneralLinearGroup | InvertibleMatrices | * | |
HeisenbergGroup | HeisenbergMatrices | * | |
OrthogonalGroup | OrthogonalMatrices | * | This can be interpreted as all rotations and reflections. |
PowerLieGroup | PowerManifold | โ | ^ is a constructor |
ProductLieGroup | ProductManifold | โ | ร of two Lie groups is a constructor |
LeftSemidirectProductLieGroup | ProductManifold | โ | โ of 2 Lie groups is a constructor, similarly โ for the right variant |
SpecialEuclideanGroup | Rotations โ Euclidean | โ | Analogously you can also use a โ if you prefer tuples (t,R) having the rotation matrix in the second component |
SpecialOrthogonalGroup | Rotations | * | |
SpecialUnitaryGroup | GeneralUnitaryMatrices | * | |
SymplecticGroup | SymplecticMatrices | * | |
TranslationGroup | Euclidean | + | |
UnitaryGroup | UnitaryMatrices | * |