  Electron energy bands of crystalline solids generically exhibit degeneracies
called band-structure nodes. Here, we introduce non-Abelian topological charges
that characterize line nodes inside the momentum space of crystalline metals
with space-time inversion ($\mathcal{PT}$) symmetry and with weak spinorbit
coupling. We show that these are quaternion charges, similar to those
describing disclinations in biaxial nematics. Starting from two-band
considerations, we develop the complete many-band description of nodes in the
presence of $\mathcal{PT}$ and mirror symmetries, which allows us to
investigate the topological stability of nodal chains in metals. The
non-Abelian charges put strict constraints on the possible nodal-line
configurations. Our analysis goes beyond the standard approach to band topology
and implies the existence of one-dimensional topological phases not present in
existing classifications.
