We construct N-complexes of non-completely antisymmetric irreducible tensor fields on D which generalize the usual complex (N=2) of differential forms. Although, for N>= 3, the generalized cohomology of these N-complexes is nontrivial, we prove a generalization of the Poincaré lemma. To that end we use a technique reminiscent of the Green ansatz for parastatistics. Several results which appeared in various contexts are shown to be particular cases of this generalized Poincaré lemma. We furthermore identify the nontrivial part of the generalized cohomology. Many of the results presented here were announced in .
Communications in Mathematical Physics
- Pub Date:
- Mathematics - Quantum Algebra;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- Mathematical Physics
- 47 pages