  Examples of non-hermitian quantum systems admitting topological insulator
phase are presented in one, two and three space dimensions. All of these
non-hermitian Hamiltonians have entirely real bulk eigenvalues and unitarity is
maintained with the introduction of appropriate inner-products in the
corresponding Hilbert spaces. The topological invariant characterizing a
particular phase is shown to be identical for a non-hermitian Hamiltonian and
its hermitian counterpart, to which it is related through a non-unitary
similarity transformation. A classification scheme for topological insulator
phases in pseudo-hermitian quantum systems is suggested.
