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
Дата:2008
Автори: Vinet, L., Zhedanov, A.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2008
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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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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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