  The Kepler space telescope has provided time series of red giants of such
unprecedented quality that a detailed asteroseismic analysis becomes possible.
For a limited set of about a dozen red giants, the observed oscillation
frequencies obtained by peak-bagging together with the most recent pulsation
codes allowed us to reliably determine the core/envelope rotation ratio. The
results so far show that the current models are unable to reproduce the
rotation ratios, predicting higher values than what is observed and thus
indicating that an efficient angular momentum transport mechanism should be at
work. Here we provide an asteroseismic analysis of a sample of 13
low-luminosity low-mass red giant stars observed by Kepler during its first
nominal mission. These targets form a subsample of the 19 red giants studied
previously Corsaro et al. 2015, which not only have a large number of extracted
oscillation frequencies, but also unambiguous mode identifications We aim to
extend the sample of red giants for which internal rotation ratios obtained by
theoretical modeling of peak-bagged frequencies are available. We also derive
the rotation ratios using different methods, and compare the results of these
methods with each other. We built seismic models using a grid search combined
with a Nelder-Mead simplex algorithm and obtained rotation averages employing
Bayesian inference and inversion methods. We compared these averages with those
obtained using a previously developed model-independent method. We find that
the cores of the red giants in this sample are rotating 5 to 10 times faster
than their envelopes, which is consistent with earlier results. The rotation
rates computed from the different methods show good agreement for some targets,
while some discrepancies exist for others.
