RT info:eu-repo/semantics/article
T1 Poisson-Hopf algebra deformations of Lie-Hamilton systems
A1 Ballesteros Castañeda, Ángel
A1 Campoamor Stursberg, Rutwig
A1 Fernandez Saiz, Eduardo
A1 Herranz, Francisco J.
A1 Lucas Veguillas, Javier de
K1 Lie system
K1 Vessiot-Guldberg Lie algebra
K1 Hopf algebra
K1 Poisson coalgebra
K1 oscillator system
K1 position-dependent mass
K1 Riccati equation
AB Hopf algebra deformations are merged with a class of Lie systems ofHamiltonian type, the so-called Lie–Hamilton systems, to devise a novelformalism: the Poisson–Hopf algebra deformations of Lie–Hamilton systems.This approach applies to any Hopf algebra deformation of any Lie–Hamiltonsystem. Remarkably, a Hopf algebra deformation transforms a Lie–Hamiltonsystem, whose dynamic is governed by a finite-dimensional Lie algebra offunctions, into a non-Lie–Hamilton system associated with a Poisson–Hopfalgebra of functions that allows for the explicit description of its t-independentconstants of the motion from deformed Casimir functions. We illustrate ourapproach by considering the Poisson–Hopf algebra analogue of the nonstandard quantum deformation of sl(2) and its applications to deform wellknown Lie–Hamilton systems describing oscillator systems, Milne–Pinneyequations, and several types of Riccati equations. In particular, we obtaina new position-dependent mass oscillator system with a time-dependentfrequency.
PB IOP Publishing
SN 1751-8121
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/40847
UL http://uvadoc.uva.es/handle/10324/40847
LA eng
NO Journal of Physics A: Mathematical and Theoretical, 2018, vol. 51, 065202
NO Producción Científica
DS UVaDOC
RD 11-abr-2025