Minimal realization of $\ell$-conformal Galilei algebra, Pais-Uhlenbeck   oscillators and their deformation
  We present the minimal realization of the $\ell$-conformal Galilei group in 2+1 dimensions on a single complex field. The simplest Lagrangians yield the complex Pais-Uhlenbeck oscillator equations. We introduce a minimal deformation of the $\ell$=1/2 conformal Galilei (a.k.a. Schr\"odinger) algebra and construct the corresponding invariant actions. Based on a new realization of the d=1 conformal group, we find a massive extension of the near-horizon Kerr-dS/AdS metric. 
Sergey Krivonos, Olaf Lechtenfeld, Alexander Sorin
hep-th gr-qc math-ph math.MP