Tensor fields of mixed Young symmetry type and N-complexes
Dubois-Violette, Michel ; Henneaux, Marc
arXiv, 0110088 / Harvested from arXiv
Text on arXiv
We construct $N$-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ which generalize the usual complex $(N=2)$ of differential forms. Although, for $N\geq 3$, the generalized cohomology of these $N$-complexes is non trivial, we prove a generalization of the Poincar\'e 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 Poincar\'e lemma. We furthermore identify the nontrivial part of the generalized cohomology. Many of the results presented here were announced in [10].
Publié le : 2001-10-09
Classification:  Mathematics - Quantum Algebra,  General Relativity and Quantum Cosmology,  High Energy Physics - Theory,  Mathematical Physics 
@article{0110088,
     author = {Dubois-Violette, Michel and Henneaux, Marc},
     title = {Tensor fields of mixed Young symmetry type and N-complexes},
     journal = {arXiv},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0110088}
}

Dubois-Violette, Michel; Henneaux, Marc. Tensor fields of mixed Young symmetry type and N-complexes. arXiv, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/0110088/