THE MODULAR STONE–VON NEUMANN THEOREM

In this paper, we use the tools of nonabelian duality to formulate and prove a far reaching generalization of the Stone–von Neumann theorem to modular representations of actions and coactions of locally compact groups on elementary C*-algebras. This greatly extends the covariant Stone– von Neumann theorem for actions of abelian groups recently proven by L. Ismert and the second author. Our approach is based on a new result about Hilbert C*-modules that is simple to state yet is widely applicable and can be used to streamline many previous arguments, so it represents an improvement, in terms of both efficiency and generality, in a long line of results in this area of mathematical physics that goes back to J. von Neumann’s proof of the classical Stone–von Neumann theorem.