  We investigate the ground state properties of a spin-1 kagome
antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain
the energy per site {$e_0=-1.41090(2)$ with $D^*=8$ multiplets retained (i.e.,
a bond dimension of $D=24$), and $e_0=-1.4116(4)$ from large-$D$
extrapolation,} by accurate TN calculations directly in the thermodynamic
limit. The symmetry between the two kinds of triangles is spontaneously broken,
with a relative energy difference of $\delta \approx$ 19\%, i.e, there is a
trimerization (simplex) valence-bond order in the ground state. The spin-spin,
dimer-dimer, and chirality-chirality correlation functions are found to decay
exponentially with a rather short correlation length, showing that the ground
state is gapped. We thus identify the ground state be a simplex valence-bond
crystal (SVBC). We also discuss the spin-1 bilinear-biquadratic Heisenberg
model on a kagome lattice, and determine its ground state phase diagram.
Moreover, we implement non-abelian symmetries, here spin SU(2), in the TN
algorithm, which improves the efficiency greatly and provides insight into the
tensor structures.
