Proper noun
the Heisenberg group
(mathematics) The group of 3×3 upper triangular matrices of the form
(
1
a
c
0
1
b
0
0
1
)
{\displaystyle {\begin{pmatrix}1&a&c\\0&1&b\\0&0&1\\\end{pmatrix}}}
under the operation of matrix multiplication, arising in the description of one-dimensional quantum-mechanical systems.
The position and momentum in this phase space are mapped to the generators of the Heisenberg group, and the Hilbert space appears as a group representation of the Heisenberg group. Source: Internet