In this paper (arXiv:1302.0684) the quantum deformations of (anti-)de Sitter  (A)dS algebras in (2+1) dimensions are revisited. In particular, the classification problem of (2+1) (A)dS Lie bialgebras is presented and the associated noncommutative quantum (A)dS spaces are also analysed. Moreover, the flat limit (or vanishing cosmological constant) of all these structures leading to (2+1) quantum Poincaré algebras is studied. Some results on the analogous (3+1) problem are sketched.

This new paper (arXiv:1212.3809) deals with a systematic computational approach for the explicit construction of any quantum Hopf algebra starting from the Lie bialgebra that gives the first-order deformation of the coproduct map. The procedure is based on the fact that any quantum algebra can be viewed as the quantization of a unique Poisson-Lie structure on the dual group.

In this paper (arXiv:1207.0071) a new integrable generalization on the two-dimensional sphere and the hyperbolic plane of the Euclidean anisotropic oscillator Hamiltonian with “centrifugal” terms is presented. The dynamical features arising from the introduction of a curved background are highlighted, and the superintegrability properties of the Hamiltonian are studied.

In the new paper “Comment on “new integrable family in n-dimensional homogeneous Lotka-Volterra systems with Abelian Lie Algebra” [J. Phys. Soc. Jpn. 72 (2003) 973]” we present the new (generalized) Poisson structure and the Hamiltonian functions for the so-called generalized ladder system (GLS), obtaining also its first integrals as functionally independent Casimir functions for the associated Poisson algebra and thus proving the complete Liouville integrability of the GLS.

In this paper (arXiv:1202.2077) 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 complete classification of real three-dimensional Lie bialgebras given in [X. Gomez, J. Math. Phys. vol. 41, p. 4939 (2000)]. Many of these 3D Poisson-Lie groups are non-coboundary structures, whose Poisson brackets are given here for the first time. Casimir functions for all three-dimensional PL groups are given, and some features of several PL structures are commented.