LAUSR

In this paper, we formulate and prove a version of the Stone–von Neumann Theorem for every $$ C^{*} $$ -dynamical system of the form $$ \left( G,{\mathbb {K}} \left( {\mathcal {H}} \right) ,\alpha \right) $$ , where G is a locally compact Hausdorff abelian group and $$ {\mathcal {H}}$$ is a Hilbert space. The novelty of our work stems from our representation of the Weyl Commutation Relation on Hilbert $$ {\mathbb {K}} \left( {\mathcal {H}} \right) $$ -modules, instead of just Hilbert spaces, and our introduction of two additional commutation relations, which are necessary to obtain a uniqueness theorem. Along the way, we apply one of our basic results on Hilbert $$ C^{*} $$ -modules to significantly shorten the length of Iain Raeburn’s well-known proof of Takai–Takesaki Duality.