Non-Hermitian band topology with generalized inversion symmetry

Non-Hermitian skin effects and exceptional points are topological phenomena characterized by integer winding numbers. In this study, we give methods to theoretically detect generalizing inversion symmetry. The generalization of symmetry is unique non-Hermitian systems. We show that parities the numbers can be determined from energy eigenvalues on inversion-invariant momenta when generalized present. simple expressions for allow us easily analyze in bands. also demonstrate (second-order) using lattice models.