Quasi-Linear Algebras and Integrability (the Heisenberg Picture)

Luc Vinet ; Alexei Zhedanov

Symmetry, integrability and geometry: methods and applications, Tome 4 (2008)

Résumé

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.

Détail

Keywords: Lie algebras; Poisson algebras; nonlinear algebras; Askey–Wilson algebra; Dolan–Grady relations.

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