A Z2-topological index as a Z2-state index

Within the setting of infinite-dimensional self-dual CAR C* algebras describing fermions in [Formula: see text] lattice, we depart from well-known Araki–Evans index for quasi-free fermion states and rewrite it terms rather than basis projections. Furthermore, reformulate results that relate equivalences Fock representations to parity into Gel’fand–Naimark–Segal associated parity.