93 citations · 2.1k across the 117 of their papers we have counts for
49 papers · 1 filter
A general approach to noncommutative spaces from Poisson homogeneous spaces: Applications to (A)dS and Poincaré
Angel Ballesteros, Ivan Gutierrez-Sagredo, Francisco J. Herranz
In this contribution we present a general procedure that allows the construction of noncommutative spaces with quantum group invariance as the quantization of their associated cois…
Shannon information entropy for a quantum nonlinear oscillator on a space of non-constant curvature
Angel Ballesteros, Ivan Gutierrez-Sagredo
The so-called Darboux III oscillator is an exactly solvable -dimensional nonlinear oscillator defined on a radially symmetric space with non-constant negative curvature. This os…
Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
Angel Ballesteros, Ivan Gutierrez-Sagredo, Francisco J. Herranz
The complete classification of classical -matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincaré groups such that their Lorentz sector is a quantum…
Poisson-Hopf deformations of Lie-Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra
Angel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz +2
The formalism for Poisson-Hopf (PH) deformations of Lie-Hamilton systems is refined in one of its crucial points concerning applications, namely the obtention of effective and comp…
Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces
Angel Ballesteros, Ivan Gutierrez-Sagredo, Flavio Mercati
Quantum homogeneous spaces are noncommutative spaces with quantum group covariance. Their semiclassical counterparts are Poisson homogeneous spaces, which are quotient manifolds of…
The -(A)dS noncommutative spacetime
Angel Ballesteros, Ivan Gutierrez-Sagredo, Francisco J. Herranz
The (3+1)-dimensional -(A)dS noncommutative spacetime is explicitly constructed by quantizing its semiclassical counterpart, which is the -(A)dS Poisson homogeneous space. Th…
Curvature as an integrable deformation
Angel Ballesteros, Alfonso Blasco, Francisco J. Herranz
The generalization of (super)integrable Euclidean classical Hamiltonian systems to the two-dimensional sphere and the hyperbolic space by preserving their (super)integrability prop…
Cayley-Klein Poisson homogeneous spaces
Francisco J. Herranz, Angel Ballesteros, Ivan Gutierrez-Sagredo +1
The nine two-dimensional Cayley-Klein geometries are firstly reviewed by following a graded contraction approach. Each geometry is considered as a set of three symmetrical homogene…
Drinfel'd double structures for Poincaré and Euclidean groups
Ivan Gutierrez-Sagredo, Angel Ballesteros, Francisco J. Herranz
All non-isomorphic three-dimensional Poisson homogeneous Euclidean spaces are constructed and analyzed, based on the classification of coboundary Lie bialgebra structures of the Eu…
The Poincaré group as a Drinfel'd double
Angel Ballesteros, Ivan Gutierrez-Sagredo, Francisco J. Herranz
The eight nonisomorphic Drinfel'd double (DD) structures for the Poincaré Lie group in (2+1) dimensions are explicitly constructed in the kinematical basis. Also, the two existing…
Global versus local superintegrability of nonlinear oscillators
Stephen C. Anco, Angel Ballesteros, Maria Luz Gandarias
Liouville (super)integrability of a Hamiltonian system of differential equations is based on the existence of globally well-defined constants of the motion, while Lie point symmetr…
A unified approach to Poisson-Hopf deformations of Lie-Hamilton systems based on sl(2)
Angel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz +2
Based on a recently developed procedure to construct Poisson-Hopf deformations of Lie-Hamilton systems, a novel unified approach to nonequivalent deformations of Lie-Hamilton syste…
Poisson-Hopf algebra deformations of Lie-Hamilton systems
Angel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz +2
Hopf algebra deformations are merged with a class of Lie systems of Hamiltonian type, the so-called Lie-Hamilton systems, to devise a novel formalism: the Poisson-Hopf algebra defo…
AdS Poisson homogeneous spaces and Drinfel'd doubles
Angel Ballesteros, Catherine Meusburger, Pedro Naranjo
The correspondence between Poisson homogeneous spaces over a Poisson-Lie group and Lagrangian Lie subalgebras of the classical double is revisited and explor…
Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations
Angel Ballesteros, Juan Carlos Marrero, Zohreh Ravanpak
Given a Lie-Poisson completely integrable bi-Hamiltonian system on , we present a method which allows us to construct, under certain conditions, a completely integrab…
The classical Darboux III oscillator: factorization, Spectrum Generating Algebra and solution to the equations of motion
Angel Ballesteros, Alberto Enciso, Francisco J. Herranz +3
In a recent paper the so-called Spectrum Generating Algebra (SGA) technique has been applied to the N-dimensional Taub-NUT system, a maximally superintegrable Hamiltonian system wh…
An exactly solvable deformation of the Coulomb problem associated with the Taub-NUT metric
Angel Ballesteros, Alberto Enciso, Francisco J. Herranz +2
In this paper we quantize the -dimensional classical Hamiltonian system , that can be regarded as a deformation of the Coulomb prob…
Lie-Hamilton systems on the plane: properties, classification and applications
A. Ballesteros, A. Blasco, F. J. Herranz +2
We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a -dependent vector field taking values in a fin…
From constants of motion to superposition rules for Lie-Hamilton systems
A. Ballesteros, J. F. Cariñena, F. J. Herranz +2
A Lie system is a nonautonomous system of first-order differential equations possessing a superposition rule, i.e. a map expressing its general solution in terms of a generic finit…
Drinfel'd doubles for (2+1)-gravity
Angel Ballesteros, Francisco J. Herranz, Catherine Meusburger
All possible Drinfel'd double structures for the anti-de Sitter Lie algebra so(2,2) and de Sitter Lie algebra so(3,1) in (2+1)-dimensions are explicitly constructed and analysed in…
Quantum algebras as quantizations of dual Poisson-Lie groups
Angel Ballesteros, Fabio Musso
A systematic computational approach for the explicit construction of any quantum Hopf algebra (U_z(g),Δ_z) starting from the Lie bialgebra (g,δ) that gives the first-order deformat…
Classification of real three-dimensional Poisson-Lie groups
Angel Ballesteros, Alfonso Blasco, Fabio Musso
All real three dimensional Poisson-Lie groups are explicitly constructed and fully classified under group automorphisms by making use of their one-to-one correspondence with the co…
Non-coboundary Poisson-Lie structures on the book group
Angel Ballesteros, Alfonso Blasco, Fabio Musso
All possible Poisson-Lie (PL) structures on the 3D real Lie group generated by a dilation and two commuting translations are obtained. Its classification is fully performed by rela…
Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform
Angel Ballesteros, Alberto Enciso, Francisco J. Herranz +2
The Stäckel transform is applied to the geodesic motion on Euclidean space, through the harmonic oscillator and Kepler-Coloumb potentials, in order to obtain maximally superintegra…