• Corpus ID: 237572018

The Modular Stone-von Neumann Theorem

  title={The Modular Stone-von Neumann Theorem},
  author={Lucas Hall and Leonard T. Huang and John Quigg},
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… 


A Generalization of the Stone–Von Neumann Theorem to Nonregular Representations of the CCR-Algebra
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 the
Covariant representations of Hecke algebras and imprimitivity for crossed products by homogeneous spaces
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) by
Wigner's theorem in Hilbert C^*-modules over C^*-algebras of compact operators
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-valued
Categorical Landstad duality for actions
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 a
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) irreducible
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 whenever
On a class of module maps of Hilbert C ∗ -modules
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 the
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 $$ \left( G,{\mathbb {K}} \left( {\mathcal {H}} \right) ,\alpha
Morita Equivalence and Continuous-Trace $C^*$-Algebras
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 actions
Pure Semigroups of Isometries on Hilbert C*-Modules
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 with