On a Z3-graded generalization of the Witten index Original Research Article

We construct a realization of the algebra of the Z3-graded topological symmetry of type (1,1,1) in terms of a pair of operators D1:H1→H2, D2:H2→H3 satisfying [D1D1†,D2†D2]=0. We show that the sequence of the restriction of these operators to the zero-energy subspace forms a complex and establish the equality of the corresponding topological invariants with the analytic indices of these operators.