Timeline for Irreducible representations of Heisenberg algebra
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Sep 15, 2015 at 20:34 | history | edited | Guntram | CC BY-SA 3.0 |
corrected typos
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| Jun 14, 2010 at 23:35 | vote | accept | Yousef | ||
| Jun 12, 2010 at 3:51 | answer | added | S. Carnahan♦ | timeline score: 5 | |
| Jun 11, 2010 at 20:30 | comment | added | Yousef | Scott: Yesy I actually not sure but I will start with $z$ acts trivially i.e. by a non zero scalar. Victor Protsak: $K$ is with zero charactristic. | |
| Jun 11, 2010 at 20:24 | history | edited | Yousef | CC BY-SA 2.5 |
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| Jun 11, 2010 at 6:43 | comment | added | S. Carnahan♦ | Upon further reflection, I don't think there is a meaningful notion of representation of a K-Lie algebra on a non-K vector space. Please disregard the last half of the last sentence in my last comment. | |
| Jun 11, 2010 at 3:01 | comment | added | Victor Protsak | To emphasize what Scott was saying, there are at least two completely different "representation theories" of Heisenberg algebra: (1) algebraic representations (which correspond to representations of the Heisenberg group as an algebraic group) and (2) unitary representations. Details of both theories depend on whether (a) $K$ is a local field of characteristic 0 (b) $K$ is finite (c) $K$ is a local field of positive characteristic. | |
| Jun 11, 2010 at 2:15 | comment | added | S. Carnahan♦ | Do you want representations for which $z$ acts by a nonzero scalar, or arbitrary representations? Most of the theory, e.g., Stone-von-Neumann theorem, only applies to central representations. Also, does your ground field have characteristic zero, and are you only considering representations on complex vector spaces? | |
| Jun 11, 2010 at 0:31 | history | edited | Yousef | CC BY-SA 2.5 |
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| Jun 10, 2010 at 14:10 | comment | added | Tim van Beek | Do you mean the "canonical commutation relations"? If that is the case, maybe Petz:"An Invitation to the Algebra of Canonical Commutation Relations" could help? Or are you looking for something more advanced/particular? | |
| Jun 9, 2010 at 23:36 | history | edited | Wadim Zudilin | CC BY-SA 2.5 |
typos fixed
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| Jun 9, 2010 at 23:34 | comment | added | S. Carnahan♦ | Which Heisenberg algebra? | |
| Jun 9, 2010 at 23:32 | comment | added | Steve Huntsman | springerlink.com/content/kl6g82r836g23n82 | |
| Jun 9, 2010 at 23:22 | history | asked | Yousef | CC BY-SA 2.5 |