approach, as Hopf algebra methods appear as a branch of quantum gravity research in their own right [@maj]. Concerning the relation of DSR to Loop Quantum Gravity, in [@abl] there is a rather heuristic derivation of modified energy-momentum relations, inherent to DSR, from spatial discreteness, but it is also explained that a violation of Lorentz invariance can neither be derived nor excluded from the present form of Loop Quantum Gravity.

Although DSR is supposed to reproduce gravitational effects in the quantum gravity regime, it is an open issue, how it compares to classical gravity. One may ask whether its low energy limit should be in accordance with the effects of a classical gravitational field, the low energy limit of quantum gravity.

In the literature there are essentially two different points of view, relating DRS to different partial aspects of full General Relativity (GR):

-   No relation to classical gravity is proposed in [@top], where DSR represents the topological degrees of freedom of the gravitational field, i.e. the remnant, when the local degrees of freedom of the gravitational field is removed. This approach is supported by the successful formulation of 2+1 gravity, well known to be a topological theory, as kind 