  We present Planck LFI frequency sky maps derived within the BeyondPlanck
framework. This framework draws samples from a global posterior distribution
that includes instrumental, astrophysical and cosmological parameters, and the
main product is an entire ensemble of frequency sky map samples. This ensemble
allows for computationally convenient end-to-end propagation of low-level
instrumental uncertainties into higher-level science products. We show that the
two dominant sources of LFI instrumental systematic uncertainties are
correlated noise and gain fluctuations, and the products presented here support
- for the first time - full Bayesian error propagation for these effects at
full angular resolution. We compare our posterior mean maps with traditional
frequency maps delivered by the Planck collaboration, and find generally good
agreement. The most important quality improvement is due to significantly lower
calibration uncertainties in the new processing, as we find a fractional
absolute calibration uncertainty at 70 GHz of $\delta g_{0}/g_{0} =5 \cdot
10^{-5}$, which is nominally 40 times smaller than that reported by Planck
2018. However, the original Planck 2018 estimate has a non-trivial statistical
interpretation, and this further illustrates the advantage of the new framework
in terms of producing self-consistent and well-defined error estimates of all
involved quantities without the need of ad hoc uncertainty contributions. We
describe how low-resolution data products, including dense pixel-pixel
covariance matrices, may be produced directly from the posterior samples
without the need for computationally expensive analytic calculations or
simulations. We conclude that posterior-based frequency map sampling provides
unique capabilities in terms of low-level systematics modelling and error
propagation, and may play an important role for future CMB B-mode experiments.
(Abridged.)
