\(\mathbb{Z}_ 3\)-graded exterior differential calculus and gauge theories of higher order (Q1912765)

The author gives a generalization of the exterior calculus based on an operator \(d\) such that \(d^3 = 0\) but \(d^2 \neq 0\), and on the cubic roots of unity. The resulting \(\mathbb{Z}_3 \)-graded algebra is related to the invariants of the ordinary gauge field tensor and its covariant derivatives.