On non-local representations of the ageing algebra in $d\geq 1$   dimensions
  Non-local representations of the ageing algebra for generic dynamical exponents $z$ and for any space dimension $d\geq 1$ are constructed. The mechanism for the closure of the Lie algebra is explained. The Lie algebra generators contain higher-order differential operators or the Riesz fractional derivative. Co-variant two-time response functions are derived. An application to phase-separation in the conserved spherical model is described. 
Stoimen Stoimenov and Malte Henkel
cond-mat.stat-mech math-ph math.MP