  The two-dimensional SU(N) quantum antiferromagnet, a generalization of the
quantum Heisenberg model, is investigated by quantum Monte Carlo simulations.
The ground state for $N\le 4$ is found to be of the N\'eel type with broken
SU(N) symmetry, whereas it is of the Spin-Peierls type for $N\ge 5$ with broken
lattice translational invariance. No intermediate spin-liquid phase was
observed in contrast to previous numerical simulations on smaller lattices
[Santoro et al., Phys. Rev. Lett. {\bf 83} 3065 (1999)].
