Heisenberg group

In mathematics, the Heisenberg group, named after Werner Heisenberg, is a group of 3×3 upper triangular matrices of the form

Related Topics:
Mathematics - Werner Heisenberg - Group - Upper triangular matrices

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:egin{pmatrix}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

1 & a & c\

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

0 & 1 & b\

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

0 & 0 & 1\

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

end{pmatrix}.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Elements a,b,c can be taken from some () commutative ring.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~