  Following an earlier construction of exactly soluble lattice models for
abelian fractional topological insulators in two and three dimensions, we
construct here an exactly soluble lattice model for a non-abelian $\nu=1$
quantum Hall state and a non-abelian topological insulator in two dimensions.
We show that both models are topologically ordered, exhibiting fractionalized
charge, ground state degeneracy on the torus and protected edge modes. The
models feature non-abelian vortices which carry fractional electric charge in
the quantum Hall case and spin in the topological insulator case. We analyze
the statistical properties of the excitations in detail and discuss the
possibility of extending this construction to 3D non-abelian topological
insulators.
