  Recent theoretical studies raised the possibility of a realization of spin
nematic states in the S=1 triangular lattice compound NiGa_2S_4. We study the
bilinear-biquadratic spin 1 chain in a zig-zag geometry by means of the density
matrix renormalization group method and exact diagonalization. We present the
phase diagram focusing on antiferromagnetic interactions. Adjacent to the known
Haldane-double Haldane and the extended critical phase with dominant spin
nematic correlations we find a trimerized phase with a nonvanishing energy gap.
We discuss results for different order parameters, energy gaps, correlation
functions, and the central charge, and make connection to field theoretical
predictions for the phase diagram.
