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'...
Збережено в:
Дата: | 2008 |
---|---|
Автори: | , |
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 |
Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
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 Ukraineid |
irk-123456789-148977 |
---|---|
record_format |
dspace |
fulltext |
|
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 |
_version_ |
1837475636672724992 |