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arXiv · 0802.0744

Quasi-Linear Algebras and Integrability (the Heisenberg Picture)

Luc Vinet·Alexei Zhedanov
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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.

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BibTeXRIS

Luc Vinet, Alexei Zhedanov. 2008-02-06. Quasi-Linear Algebras and Integrability (the Heisenberg Picture). https://doi.org/10.3842/sigma.2008.015

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