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

PI Lara Ismert

This is a collaborative work with Leonard Huang, Ph.D. at the University of Nevada, Reno.

In this paper, we formulate and prove a version of the Stone-von Neumann Theorem for every C*-dynamical system of the form (G,K(H),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 K(H)-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.

Research Dates

06/01/2018 to 09/01/2019

Researchers

  • Lara M. Ismert

    Lara M. Ismert

    Department
    Mathematics Department
    Degrees
    Ph.D., M.S., University of Nebraska-Lincoln

Categories: Faculty-Staff