An overview of Lie groups
Alphabetical list of Lie groups
Group | Manifold | $∘$ | Comment |
---|---|---|---|
GeneralLinearGroup | InvertibleMatrices | * | |
HeisenbergGroup | HeisenbergMatrices | * | |
OrthogonalGroup | OrthogonalMatrices | * | This can be interpreted as all rotations and reflections. |
SpecialEuclideanGroup | Rotations ⋉ Euclidean | ∘ | Analogously you can also use a ⋊ if you prefer tuples (t,R) having the rotation matrix in the second component |
SpecialOrthogonalGroup | Rotations | * | |
SpecialUnitaryGroup | GeneralUnitaryMatrices | * | |
TranslationGroup | Euclidean | + | |
UnitaryGroup | UnitaryMatrices | * |