  In this paper, we investigate topological properties of the ground state of
the SU(N) Heisenberg chain, which is argued to be relevant to the
Mott-insulating phase of alkaline-earth cold fermions in a one-dimensional
optical lattice. By calculating the entanglement spectrum, we show that the
ground state is in one of the topological phases protected by SU(N) symmetry.
We then discuss an alternative characterization of it with non-local string
order parameters. We also consider how the reduction of the protecting symmetry
affects the topological phase paying particular attention to the entanglement
spectrum.
