Quasi-Linear Algebras and Integrability (the Heisenberg Picture)
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'' . We show that many algebras with nonlinear commutation relations such as the Askey-Wilson, -Dolan-Grady and others satisfy this property. This provides one more (explicit Heisenberg evolution) interpretation of the corresponding integrable systems.
Keywords
Cite
@article{arxiv.0802.0744,
title = {Quasi-Linear Algebras and Integrability (the Heisenberg Picture)},
author = {Luc Vinet and Alexei Zhedanov},
journal= {arXiv preprint arXiv:0802.0744},
year = {2008}
}
Comments
This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/