Dynamical realizations of $\mathcal {N}=1$N=1 l-conformal Galilei superalgebra

Abstract

Dynamical systems which are invariant under \documentclass[12pt]{minimal}\begin{document}$\mathcal {N}=1$\end{document}N=1 supersymmetric extension of the l-conformal Galilei algebra are constructed. These include a free \documentclass[12pt]{minimal}\begin{document}$\mathcal {N}=1$\end{document}N=1 superparticle which is governed by higher derivative equations of motion and an \documentclass[12pt]{minimal}\begin{document}$\mathcal {N}=1$\end{document}N=1 supersymmetric Pais-Uhlenbeck oscillator for a particular choice of its frequencies. A Niederer-like transformation which links the models is proposed.