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'...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
National Academy of Science of Ukraine
2008-02-01
|
| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2008.015 |
| _version_ | 1819096976644374528 |
|---|---|
| author | Alexei Zhedanov Luc Vinet |
| author_facet | Alexei Zhedanov Luc Vinet |
| author_sort | Alexei Zhedanov |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-22T00:07:45Z |
| format | Article |
| id | doaj.art-35f768f23cc84d679a732d0504bab479 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-22T00:07:45Z |
| publishDate | 2008-02-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-35f768f23cc84d679a732d0504bab4792022-12-21T18:45:32ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592008-02-014015Quasi-Linear Algebras and Integrability (the Heisenberg Picture)Alexei ZhedanovLuc VinetWe 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.http://dx.doi.org/10.3842/SIGMA.2008.015Lie algebrasPoisson algebrasnonlinear algebrasAskey-Wilson algebraDolan-Grady relations |
| spellingShingle | Alexei Zhedanov Luc Vinet Quasi-Linear Algebras and Integrability (the Heisenberg Picture) Symmetry, Integrability and Geometry: Methods and Applications Lie algebras Poisson algebras nonlinear algebras Askey-Wilson algebra Dolan-Grady relations |
| 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 |
| topic | Lie algebras Poisson algebras nonlinear algebras Askey-Wilson algebra Dolan-Grady relations |
| url | http://dx.doi.org/10.3842/SIGMA.2008.015 |
| work_keys_str_mv | AT alexeizhedanov quasilinearalgebrasandintegrabilitytheheisenbergpicture AT lucvinet quasilinearalgebrasandintegrabilitytheheisenbergpicture |