Heisenberg Group

The Heisenberg group – named after Werner Heisenberg – of 3×3 upper triangular matrices historically originates in and still has its strongest ties to quantum physics: there it is a group of unitary operators acting on the space of states induced from those observables on a linear phase space – a symplectic vector space – which are given by linear or by constant functions. So any Heisenberg group is a subgroup of a group of observables in certain simple examples of quantum mechanical systems.
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