Heisenberg group

The term Heisenberg group is a contextual term used typically to refer to a unitriangular matrix group of degree three over a suitable field or commutative unital ring. Particular uses of the term are:

• Continuous Heisenberg group refers to unitriangular matrix group:UT(3,R) -- the group over the field of real numbers.
• Discrete Heisenberg group or integral Heisenberg group refers to unitriangular matrix group:UT(3,Z) -- the group over the ring of integers.