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This article is cited in 11 scientific papers (total in 11 papers)
Quasi-Linear Algebras and Integrability (the Heisenberg Picture)
Luc Vineta, Alexei Zhedanovb a Université de Montréal PO Box 6128, Station Centre-ville, Montréal QC H3C 3J7, Canada
b Donetsk Institute for Physics and Technology, Donetsk 83114, Ukraine
Abstract:
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.
Keywords:
Lie algebras; Poisson algebras; nonlinear algebras; Askey–Wilson algebra; Dolan–Grady relations.
Received: November 16, 2007; in final form January 19, 2008; Published online February 6, 2008
Citation:
Luc Vinet, Alexei Zhedanov, “Quasi-Linear Algebras and Integrability (the Heisenberg Picture)”, SIGMA, 4 (2008), 015, 22 pp.
Linking options:
https://www.mathnet.ru/eng/sigma268 https://www.mathnet.ru/eng/sigma/v4/p15
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Abstract page: | 295 | Full-text PDF : | 45 | References: | 43 |
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