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Let G be a non-compact real algebraic group and Γ < G a lattice. One purpose of this paper is to show that there is a smooth, volume preserving, mixing action of G or Γ on a compact manifold which admits a smooth deformation. In fact, we prove a stronger statement by exhibiting large finite dimensional spaces of deformations. We also describe some other, rather special, deformations when G = SO(1, n).doi:10.1090/s0002-9947-07-04372-3 fatcat:t5nexzjiqbfvpfro2jrijsavmy