Quasi-Linear Algebras and Integrability (the Heisenberg Picture)
We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables (operators) as functions of ''time'...
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| Datum: | 2008 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2008
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/148977 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Quasi-Linear Algebras and Integrability (the Heisenberg Picture) / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 29 назв. — англ. |
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irk-123456789-1489772019-02-20T01:25:53Z Quasi-Linear Algebras and Integrability (the Heisenberg Picture) Vinet, L. Zhedanov, A. We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables (operators) as functions of ''time'' t. We show that many algebras with nonlinear commutation relations such as the Askey-Wilson, q-Dolan-Grady and others satisfy this property. This provides one more (explicit Heisenberg evolution) interpretation of the corresponding integrable systems. 2008 Article Quasi-Linear Algebras and Integrability (the Heisenberg Picture) / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 29 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 17B63; 17B37; 47L90 http://dspace.nbuv.gov.ua/handle/123456789/148977 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables (operators) as functions of ''time'' t. We show that many algebras with nonlinear commutation relations such as the Askey-Wilson, q-Dolan-Grady and others satisfy this property. This provides one more (explicit Heisenberg evolution) interpretation of the corresponding integrable systems. |
| format |
Article |
| author |
Vinet, L. Zhedanov, A. |
| spellingShingle |
Vinet, L. Zhedanov, A. Quasi-Linear Algebras and Integrability (the Heisenberg Picture) Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Vinet, L. Zhedanov, A. |
| author_sort |
Vinet, L. |
| title |
Quasi-Linear Algebras and Integrability (the Heisenberg Picture) |
| title_short |
Quasi-Linear Algebras and Integrability (the Heisenberg Picture) |
| title_full |
Quasi-Linear Algebras and Integrability (the Heisenberg Picture) |
| title_fullStr |
Quasi-Linear Algebras and Integrability (the Heisenberg Picture) |
| title_full_unstemmed |
Quasi-Linear Algebras and Integrability (the Heisenberg Picture) |
| title_sort |
quasi-linear algebras and integrability (the heisenberg picture) |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148977 |
| citation_txt |
Quasi-Linear Algebras and Integrability (the Heisenberg Picture) / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 29 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT vinetl quasilinearalgebrasandintegrabilitytheheisenbergpicture AT zhedanova quasilinearalgebrasandintegrabilitytheheisenbergpicture |
| first_indexed |
2025-07-12T20:48:41Z |
| last_indexed |
2025-07-12T20:48:41Z |
| _version_ |
1837475636672724992 |