The kappa-(A)dS quantum algebra in (3+1) dimensions

In this paper (arXiv:1612.03169) the quantum duality principle is used to obtain explicitly the Poisson analogue of the kappa-(A)dS quantum algebra in (3+1) dimensions as the corresponding Poisson-Lie structure on the dual solvable Lie group. The construction is fully performed in a kinematical basis and deformed Casimir functions are also explicitly obtained. The cosmological constant Λ is included as a Poisson-Lie group contraction parameter, and the limit Λ0 leads to the well-known kappa-Poincaré algebra in the bicrossproduct basis. A twisted version with Drinfel’d double structure of this kappa-(A)dS deformation is sketched.

Open call for a research position

An one-year position starting on January, 2017, is available in our group. The deadline for applications will be December 8th. Candidates willing to join any of the research lines of the group and with strong expertise on symbolic and/or numerical computation are encouraged to apply as soon as possible. Candidates have to be registered at the “Registro de Garantía Juvenil” and should contact us urgently at angelb@ubu.es.

Special Issue in Advances in High Energy Physics: “Planck-Scale Deformations of Relativistic Symmetries”

Submissions for an Special Issue focusing on quantum-gravity-induced deformations of relativistic symmetries, with a rather broad perspective, is already opened. Manuscripts have to be sumbitted by March 10, 2017. Advances in High Energy Physics is an open-access electronic Journal with no publishing charges. More detailed information about this Special Issue can be found here.

Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations

Given a Lie-Poisson completely integrable bi-Hamiltonian system, in the new paper arXiv:1609.07438 we present a method which allows us to construct, under certain conditions, a completely integrable bi-Hamiltonian deformation of the initial Lie-Poisson system on a non-abelian Poisson-Lie group. Moreover, we show that from the two multiplicative (Poisson-Lie) Hamiltonian structures that underly the dynamics of the deformed system and by making use of the non-abelian group law, one may obtain two completely integrable Hamiltonian systems on the direct product of the non-abelian group by itself. By construction, both systems admit reduction, via the multiplication in the non-abelian group, to the initial deformed bi-Hamiltonian system. The previous approach is applied to two relevant Lie-Poisson completely integrable bi-Hamiltonian systems: the Lorenz and Euler top systems.