Unitriangular matrix group:UT(3,R)
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This group is also sometimes called the continuous Heisenberg group or real Heisenberg group.
- The group has the natural structure of an algebraic group over the field of real numbers. (Alternatively, we can think of it as the set of -points of unitriangular matrix group:UT(3,C), which is the corresponding algebraic group over the field of complex numbers). As an algebraic group, it is a unipotent algebraic group.
- The group has the structure of a real Lie group (and hence also a topological group). The underlying manifold is diffeomorphic to .