An overview of Lie groups

Alphabetical list of Lie groups

GroupManifold$โˆ˜$Comment
GeneralLinearGroupInvertibleMatrices*
HeisenbergGroupHeisenbergMatrices*
OrthogonalGroupOrthogonalMatrices*This can be interpreted as all rotations and reflections.
PowerLieGroupPowerManifoldโˆ˜^ is a constructor
ProductLieGroupProductManifoldโˆ˜ร— of two Lie groups is a constructor
LeftSemidirectProductLieGroupProductManifoldโˆ˜โ‹‰ of 2 Lie groups is a constructor, similarly โ‹Š for the right variant
SpecialEuclideanGroupRotationsโ‹‰Euclideanโˆ˜Analogously you can also use a โ‹Š if you prefer tuples (t,R) having the rotation matrix in the second component
SpecialOrthogonalGroupRotations*
SpecialUnitaryGroupGeneralUnitaryMatrices*
SymplecticGroupSymplecticMatrices*
TranslationGroupEuclidean+
UnitaryGroupUnitaryMatrices*