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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 18th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub for [[Stone-von Neumann theorem]]

   stub for Stone-von Neumann theorem

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 22nd 2017
   • (edited Dec 22nd 2017)
   • PermaLink
   Author: Urs
   Format: MarkdownItex(years later...) I have added a few lines to the Idea secton at _[[Stone-von Neumann theorem]]_ indicating what the Schrödinger representation actually looks like, and I made "[[Schrödinger representation]]" redirect to the entry.

   (years later…)

   I have added a few lines to the Idea secton at Stone-von Neumann theorem indicating what the Schrödinger representation actually looks like, and I made “Schrödinger representation” redirect to the entry.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeApr 14th 2025
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Amritanshu Prasad]]: *An easy proof of the Stone-von Neumann-Mackey theorem*, Expositiones Mathematicae **29** (2011) 110-118 &lbrack;[arXiv:0912.0574](https://arxiv.org/abs/0912.0574), [doi:10.1016/j.exmath.2010.06.001](https://doi.org/10.1016/j.exmath.2010.06.001)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Stone-von+Neumann+theorem/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/Stone-von+Neumann+theorem/9">v9</a>, <a href="https://ncatlab.org/nlab/show/Stone-von+Neumann+theorem">current</a>

   added pointer to:

   • Amritanshu Prasad: An easy proof of the Stone-von Neumann-Mackey theorem, Expositiones Mathematicae 29 (2011) 110-118 [arXiv:0912.0574, doi:10.1016/j.exmath.2010.06.001]

   diff, v9, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeApr 14th 2025
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to the original: * [[Marshall H. Stone]]: *Linear transformations in Hilbert space. III. Operational methods and group theory*, Proceedings of the National Academy of Sciences of the United States of America, **16** (1930) 172–175 &lbrack;[jstor:85485](https://www.jstor.org/stable/85485), [doi:10.1073/pnas.16.2.172](https://doi.org/10.1073/pnas.16.2.172)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Stone-von+Neumann+theorem/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/Stone-von+Neumann+theorem/10">v10</a>, <a href="https://ncatlab.org/nlab/show/Stone-von+Neumann+theorem">current</a>

   added pointer to the original:

   • Marshall H. Stone: Linear transformations in Hilbert space. III. Operational methods and group theory, Proceedings of the National Academy of Sciences of the United States of America, 16 (1930) 172–175 [jstor:85485, doi:10.1073/pnas.16.2.172]

   diff, v10, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeApr 14th 2025
   • (edited Apr 14th 2025)
   • PermaLink
   Author: Urs
   Format: MarkdownItexand * [[George W. Mackey]]: *A theorem of Stone and von Neumann*, Duke Mathematical Journal, **16** (1949) 313–326 &lbrack;[doi:10.1215/S0012-7094-49-01631-2](https://projecteuclid.org/journals/duke-mathematical-journal/volume-16/issue-2/A-theorem-of-Stone-and-von-Neumann/10.1215/S0012-7094-49-01631-2.short)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Stone-von+Neumann+theorem/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/Stone-von+Neumann+theorem/10">v10</a>, <a href="https://ncatlab.org/nlab/show/Stone-von+Neumann+theorem">current</a>

   and

   • George W. Mackey: A theorem of Stone and von Neumann, Duke Mathematical Journal, 16 (1949) 313–326 [doi:10.1215/S0012-7094-49-01631-2]

   diff, v10, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeApr 14th 2025
   • (edited Apr 14th 2025)
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave expanded the Idea-section a fair bit ([here](https://ncatlab.org/nlab/show/Stone-von+Neumann+theorem#Idea)), mentioning Mackey's generalization to Heisenberg groups of locally compact abelian groups and the example of the integer Heisenberg group for abelian Chern-Simons theory over the torus. <a href="https://ncatlab.org/nlab/revision/diff/Stone-von+Neumann+theorem/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/Stone-von+Neumann+theorem/11">v11</a>, <a href="https://ncatlab.org/nlab/show/Stone-von+Neumann+theorem">current</a>

   have expanded the Idea-section a fair bit (here), mentioning Mackey’s generalization to Heisenberg groups of locally compact abelian groups and the example of the integer Heisenberg group for abelian Chern-Simons theory over the torus.

   diff, v11, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeApr 14th 2025
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave added a section ([here](https://ncatlab.org/nlab/show/Stone-von+Neumann+theorem#ForGeneralHeisenbergGroupsOfAbelianGroups)) with statement (following [Prasad 2011](https://ncatlab.org/nlab/show/Stone-von+Neumann+theorem#Prasad11)) of Mackey's general form of Stone-von Neumann for Heisenberg groups of locally compact abelian groups. <a href="https://ncatlab.org/nlab/revision/diff/Stone-von+Neumann+theorem/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/Stone-von+Neumann+theorem/11">v11</a>, <a href="https://ncatlab.org/nlab/show/Stone-von+Neumann+theorem">current</a>

   have added a section (here) with statement (following Prasad 2011) of Mackey’s general form of Stone-von Neumann for Heisenberg groups of locally compact abelian groups.

   diff, v11, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeApr 14th 2025
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Jonathan Rosenberg]]: *A Selective History of the Stone-von Neumann Theorem*, in: *Operator Algebras, Quantization, and Noncommutative Geometry: A Centennial Celebration Honoring John von Neumann and Marshall H. Stone*, Contemporary Mathematics **365**, AMS (2004) &lbrack;[doi:10.1090/conm/365](https://doi.org/10.1090/conm/365), [pdf](https://www.math.umd.edu/~jmr/StoneVNart.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Stone-von+Neumann+theorem/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/Stone-von+Neumann+theorem/14">v14</a>, <a href="https://ncatlab.org/nlab/show/Stone-von+Neumann+theorem">current</a>

   added pointer to:

   • Jonathan Rosenberg: A Selective History of the Stone-von Neumann Theorem, in: Operator Algebras, Quantization, and Noncommutative Geometry: A Centennial Celebration Honoring John von Neumann and Marshall H. Stone, Contemporary Mathematics 365, AMS (2004) [doi:10.1090/conm/365, pdf]

   diff, v14, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeApr 14th 2025
   • (edited Apr 14th 2025)
   • PermaLink
   Author: Urs
   Format: MarkdownItex* [[Michael Reed]], [[Barry Simon]], Thm. VIII.14 in: *Functional Analysis*, Volume I of: *Methods of Modern Mathematical Physics*, Academic Press (1978) &lbrack;[ISBN:9780125850506](https://www.elsevier.com/books/i-functional-analysis/reed/978-0-08-057048-8), [doi:10.1016/B978-0-12-585001-8.X5001-6](https://doi.org/10.1016/B978-0-12-585001-8.X5001-6), [pdf](http://www.astrosen.unam.mx/~aceves/Metodos/ebooks/reed_simon1.pdf)&rbrack; * Gérard Lion, [[Michèle Vergne]], §1.3 in: *The Weil representation, Maslov index and Theta series*, Progress in Mathematics **6**, Birkhäuser (1980) &lbrack;[doi:10.1007/978-1-4684-9154-8](https://doi.org/10.1007/978-1-4684-9154-8)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Stone-von+Neumann+theorem/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/Stone-von+Neumann+theorem/14">v14</a>, <a href="https://ncatlab.org/nlab/show/Stone-von+Neumann+theorem">current</a>

   • Michael Reed, Barry Simon, Thm. VIII.14 in: Functional Analysis, Volume I of: Methods of Modern Mathematical Physics, Academic Press (1978) [ISBN:9780125850506, doi:10.1016/B978-0-12-585001-8.X5001-6, pdf]

   • Gérard Lion, Michèle Vergne, §1.3 in: The Weil representation, Maslov index and Theta series, Progress in Mathematics 6, Birkhäuser (1980) [doi:10.1007/978-1-4684-9154-8]

   diff, v14, current