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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Бібліографічні деталі
Дата:2008
Автори: Vinet, L., Zhedanov, A.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2008
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ: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
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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spelling 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
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