The Heisenberg group H^n in n complex variables is the group of all (z, t) with z element C^n and t element R having multiplication (w, t)(z, t') = (w + z, t + t' + ℑ[w^* z]) where w^* is the adjoint. The Heisenberg group is isomorphic to the group of matrices [1 | z^* | 1/2 ( left bracketing bar z right bracketing bar )^2 + i t 0 | 1 | z 0 | 0 | 1], and satisfies (z, t)^(-1) = (-z, - t).