Quasi-Linear Algebras and Integrability (the Heisenberg Picture)

Details Quasi-Linear Algebras and Integrability (the Heisenberg Picture) Quasi-Linear Algebras and Integrability (the Heisenberg Picture)

2008-02-06

arxiv.org/abs/0802.0744v1

SIGMA 4 (2008), 015, 22 pages

Mathematics

Quantum Algebra

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (Ju

Scientific paper

10.3842/SIGMA.2008.015

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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