Fractal properties of quantum spacetime

Abstract

We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to quantum gravity. In particular we analyze the cases of a quantum sphere and of \k-Minkowski, the latter being relevant in the context of quantum gravity.Comment: 4 pages, 2 figures; some minor corrections; reference adde