Corpus ID: 237572018

The Modular Stone-von Neumann Theorem

@inproceedings{Hall2021TheMS,
title={The Modular Stone-von Neumann Theorem},
author={Lucas Hall and Leonard Huang and John Quigg},
year={2021}
}
• Lucas Hall, Leonard Huang
• Published 18 September 2021
• Mathematics, Physics
In this paper, we use the tools of nonabelian duality to formulate and prove a far-reaching generalization of the Stonevon 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… Expand

References

SHOWING 1-10 OF 36 REFERENCES
A Generalization of the Stone–Von Neumann Theorem to Nonregular Representations of the CCR-Algebra
• Mathematics
• 1999
We give a classification, up to unitary equivalence, of the representations of the C*-algebra of the Canonical Commutation Relations which generalizes the classical Stone–von Neumann Theorem to theExpand
Covariant representations of Hecke algebras and imprimitivity for crossed products by homogeneous spaces
• Mathematics
• 2005
For discrete Hecke pairs (G,H), we introduce a notion of covariant representation which reduces in the case where H is normal to the usual definition of covariance for the action of G/H on c0(G/H) byExpand
Wigner's theorem in Hilbert C^*-modules over C^*-algebras of compact operators
• Mathematics
• 2002
Let W be a Hilbert C ⁄ -module over the C ⁄ - algebra A 6 C of all compact operators on a Hilbert space. It is proved that any function T : W ! W which pre- serves the absolute value of the A-valuedExpand
• Mathematics
• 2006
Let G be a locally compact group. We show that the category A(G) of actions of G on C � -algebras (with equivari- ant nondegenerate ∗-homomorphisms into multiplier algebras) is equivalent, via aExpand
The local structure of twisted covariance algebras
The fundamental problem in investigating the unitary representation theory of a separable locally compact group G is to determine its space G ̂ of (equivalence classes of) irreducibleExpand
Crossed Products by Hecke Pairs
We develop a theory of crossed products by actions of Hecke pairs (G,Γ), motivated by applications in non-abelian C∗-duality. Our approach gives back the usual crossed product construction wheneverExpand
On a class of module maps of Hilbert C ∗ -modules
• Mathematics
• 2002
The paper describes some basic properties of a class of module maps of Hilbert C ∗ -modules. In Section 1 ideal submodules are considered and the canonical Hilbert C ∗ -module structure on theExpand
The Covariant Stone–von Neumann Theorem for Actions of Abelian Groups on $$C^{*}$$-Algebras of Compact Operators
• Mathematics, Physics
• 2020
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) ,\alphaExpand
Morita Equivalence and Continuous-Trace $C^*$-Algebras
• Mathematics
• 1998
The algebra of compact operators Hilbert $C^*$-modules Morita equivalence Sheaves, cohomology, and bundles Continuous-trace $C^*$-algebras Applications Epilogue: The Brauer group and group actionsExpand
Pure Semigroups of Isometries on Hilbert C*-Modules
• Mathematics
• 2014
We show that pure strongly continuous semigroups of adjointable isometries on a Hilbert C*-module are standard right shifts. By counter examples, we illustrate that the analogy of this result withExpand