The Modular Stone-von Neumann Theorem

2021/09/18 by Lucas Hall, Hall, Lucas, Leonard Huang +3 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2109.08997

Abstract

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.

Cited by

• The Covariant Stone-von Neumann Theorem for Locally Compact Quantum Groups

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