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We show that the UV-regime at the Lifshitz point $z=3$ is equivalent to workwith a momenta manifold whose topology is the same as that of an $AdS_2\timesS^2$ space. According to Snyder's theory, curved momentum space is related tonon-commutative quantized spacetime. In this sense, our analysis suggests anequivalence between Horava-Lifshitz and Snyder's theory.

Spectral dimension of Horava-Snyder spacetime and the $AdS_2\times S^2$ momentum space