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\\é 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\\é lemma. We furthermore identify the nontrivial part of the generalized cohomology. Many of the results presented here were announced in [10].
Publié le : 2002-07-05
Classification:
[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA],
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],
[PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc],
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
@article{hal-00013419,
author = {Henneaux, Marc and Dubois-Violette, Michel},
title = {Tensor fields of mixed Young symmetry type and N-complexes},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00013419}
}
Henneaux, Marc; Dubois-Violette, Michel. Tensor fields of mixed Young symmetry type and N-complexes. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00013419/