We consider the Moyal deformation of self-dual gravity. In the conformal
    primary basis, holomorphic collinear limits of the amplitudes of this theory
    show that it enjoys a perturbatively exact symmetry algebra $LW_\wedge$ that
    generalises $Lw_\wedge$, the loop algebra of the wedge algebra of
    $w_{1+\infty}$, which appears in self-dual gravity.

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