An easy proof of the Stone–von Neumann–Mackey Theorem

2009/12/03 by Amritanshu Prasad · 1 citation
Computer Science · Mathematics · Medicine · #Calculus (dental) #Computability, Logic, AI Algorithms #Discrete mathematics #Mathematical and Theoretical Analysis #Mathematics #Medicine #Pure mathematics #Von Neumann architecture #advanced mathematical theories #math.NT #math.RT #msc:43-01

paper · pdf · doi:10.1016/j.exmath.2010.06.001

published as Expositiones Mathematicae 29 (2011) 110-118 · 10 pages

arxiv created 2009/12/03 · openalex publication_date 2010/06/26 · arxiv updated 2011/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The Stone-von Neumann-Mackey Theorem for Heisenberg groups associated to locally compact abelian groups is proved using the Peter-Weyl theorem and the theory of Fourier transforms for finite dimensional real vector spaces. A theorem of Pontryagin and van Kampen on the structure of locally compact abelian groups (which is evident in any particular case) is assumed.

Citations

• Sur certains groupes d'opérateurs unitaires

Cited by

• Heisenberg group [wikipedia]

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• Generalize Heisenberg Groups and Self-Duality
• The Covariant Stone-von Neumann Theorem for Locally Compact Quantum Groups
• Elements of harmonic analysis, 3
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