On a Z₃-Graded Generalization of the Witten Index

الأصل · EN

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, and 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.