superconformal Newton–Hooke algebra and many-body mechanics

A representation of the conformal Newton–Hooke algebra on a phase space of n particles in arbitrary dimension which interact with one another via a generic conformal potential and experience a universal cosmological repulsion or attraction is constructed. The minimal superconformal extension of the Newton–Hooke algebra and its dynamical realization in many-body mechanics are studied.     

Eisenhart lift in pseudo–Euclidean space and higher rank killing tensors

It is emphasized that the Eisenhart lift applied to integrable systems in pseudo–Euclidean space may result in Ricci–flat metrics of ultrahyperbolic signature which admit higher rank Killing tensors.     

N = 4 Superconformal Algebra in Curved Space and Pseudo-Hyper-Kähler Geometry

We construct the representation of the small N=4 superconformal algebra in curved space under the minimal interaction assumption. We find that the structure relations of the algebra are satisfied within our assumption in the background of the metric of a pseudo-hyper-Kähler manifold.     

Dynamical realization of l-conformal Galilei algebra and oscillators

The method of nonlinear realizations is applied to the l-conformal Galilei algebra to construct a dynamical system without higher derivative terms in the equations of motion. A configuration space of the model involves coordinates, which parametrize particles in d spatial dimensions, and a conformal mode, which gives rise to an effective external field. It is shown that trajectories of the system can be mapped into those of a set of decoupled oscillators in d dimensions.