The Covariant Stone-von Neumann Theorem for Actions of Abelian Groups on C∗-Algebras of Compact Operators

In this paper, we formulate and prove a version of the Stone-von Neumann Theorem for every C∗-dynamical system of the form G,KH,α, where G is a locally compact Hausdorff abelian group and H is a Hilbert space. The novelty of our work stems from our representation of the Weyl Commutation Relation on Hilbert KH-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.