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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2008 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2008
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148977 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862727286398124032 |
|---|---|
| author | Vinet, L. Zhedanov, A. |
| author_facet | Vinet, L. Zhedanov, A. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T19:02:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148977 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:02:08Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Vinet, L. Zhedanov, A. 2019-02-19T12:22:25Z 2019-02-19T12:22:25Z 2008 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 https://nasplib.isofts.kiev.ua/handle/123456789/148977 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. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quasi-Linear Algebras and Integrability (the Heisenberg Picture) Article published earlier |
| spellingShingle | Quasi-Linear Algebras and Integrability (the Heisenberg Picture) Vinet, L. Zhedanov, A. |
| title | 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_short | Quasi-Linear Algebras and Integrability (the Heisenberg Picture) |
| title_sort | quasi-linear algebras and integrability (the heisenberg picture) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148977 |
| work_keys_str_mv | AT vinetl quasilinearalgebrasandintegrabilitytheheisenbergpicture AT zhedanova quasilinearalgebrasandintegrabilitytheheisenbergpicture |