  We extend the construction of a spectral triple for k-Minkowski space,
previously given for the two-dimensional case, to the general n-dimensional
case. This takes into account the modular group naturally arising from the
symmetries of the geometry, and requires the use of notions that have been
recently developed in the frameworks of twisted and modular spectral triples.
First we compute the spectral dimension, using an appropriate weight, and show
that in general it coincides with the classical one. We also study the
classical limit and the analytic continuation of the associated zeta function.
Then we compare this notion of dimension with the one coming from homology. To
this end, we compute the twisted Hochschild dimension of the universal
enveloping algebra underlying k-Minkowski space. The result is that twisting
avoids the dimension drop, similarly to other examples coming from quantum
groups. In particular, the simplest such twist is given by the inverse of the
modular group mentioned above.
