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Quantum structure of the motion groups of the two-dimensional Cayley-Klein geometries

- Á. Ballesteros, F. J. Herranz, M. Olmo, M. Santander
- Mathematics
- 7 November 1993

A simultaneous and global scheme of quantum deformation is defined for the set of algebras corresponding to the groups of motions of the two-dimensional Cayley-Klein geometries. Their central… Expand

Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability

- Á. Ballesteros, A. Enciso, F. J. Herranz, O. Ragnisco, D. Riglioni
- Physics
- 27 February 2011

Quantum (2+1) kinematical algebras: a global approach

- Á. Ballesteros, F. J. Herranz, M. Olmo, M. Santander
- Mathematics
- 21 February 1994

In this paper we give an approach to quantum deformations of the (2+1) kinematical Lie algebras within a scheme that simultaneously describes all groups of motions of classical geometries in N=3… Expand

Maximal superintegrability of the generalized Kepler–Coulomb system on N-dimensional curved spaces

- Á. Ballesteros, F. J. Herranz
- Physics, Mathematics
- 13 March 2009

The superposition of the Kepler–Coulomb potential on the 3D Euclidean space with three centrifugal terms has recently been shown to be maximally superintegrable (Verrier and Evans 2008 J. Math. Phys.… Expand

Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability

- J. Cariñena, F. J. Herranz, M. F. Rañada
- Mathematics
- 20 January 2017

The Eisenhart geometric formalism, which transforms an Euclidean natural Hamiltonian H = T + V into a geodesic Hamiltonian T with one additional degree of freedom, is applied to the four families of… Expand

Hamiltonian Systems Admitting a Runge–Lenz Vector and an Optimal Extension of Bertrand’s Theorem to Curved Manifolds

- Á. Ballesteros, A. Enciso, F. J. Herranz, O. Ragnisco
- Mathematics
- 6 October 2008

Bertrand’s theorem asserts that any spherically symmetric natural Hamiltonian system in Euclidean 3-space which possesses stable circular orbits and whose bounded trajectories are all periodic is… Expand

Conformal compactification of spacetimes

- F. J. Herranz, M. Santander
- Mathematics
- 9 August 2002

The conformal groups for the nine two-dimensional real spaces of constant curvature are realized as matrix groups acting as globally defined linear transformations in a four-dimensional 'conformal… Expand

Universal $R$-matrix for non-standard quantum $sl(2,\R)$

- Á. Ballesteros, F. J. Herranz
- Physics
- 11 April 1996

A universal $R$-matrix for the non-standard (Jordanian) quantum deformation of $sl(2,\R)$ is presented. A family of solutions of the quantum Yang--Baxter equation is obtained from some finite… Expand

Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

- Á. Ballesteros, N. A. Gromov, F. J. Herranz, M. Olmo, M. Santander
- Mathematics
- 9 December 1994

Lie bialgebra contractions are introduced and classified. A non‐degenerate coboundary bialgebra structure is implemented into all pseudo‐orthogonal real algebras so(p,q) starting from the one… Expand

Curved momentum spaces from quantum (anti–)de Sitter groups in (
3+1
) dimensions

- Á. Ballesteros, Giulia Gubitosi, I. Guti'errez-Sagredo, F. J. Herranz
- Mathematics, PhysicsPhysical Review D
- 14 November 2017

Curved momentum spaces associated to the $\kappa$-deformation of the (3+1) de Sitter and Anti-de Sitter algebras are constructed as orbits of suitable actions of the dual Poisson-Lie group associated… Expand

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