  We propose the concept of 2D non-Abelian topological insulator which can
explain the energy distributions of the edge states and corner states in
systems with parity-time symmetry. From the viewpoint of non-Abelian band
topology, we establish the constraints on the 2D Zak phase and polarization. We
demonstrate that the corner states in some 2D systems can be explained as the
boundary mode of the 1D edge states arising from the multi-band non-Abelian
topology of the system. We also propose the use of off-diagonal Berry phase as
complementary information to assist the prediction of edge states in
non-Abelian topological insulators. Our work provides an alternative approach
to study edge and corner modes and this idea can be extended to 3D systems.
