Generalized Cohomology for Irreducible Tensor Fields of Mixed Young Symmetry Type

@article{DuboisViolette1999GeneralizedCF,
  title={Generalized Cohomology for Irreducible Tensor Fields of Mixed Young Symmetry Type},
  author={M. Dubois-Violette and M. Henneaux},
  journal={Letters in Mathematical Physics},
  year={1999},
  volume={49},
  pages={245-252}
}
  • M. Dubois-Violette, M. Henneaux
  • Published 1999
  • Mathematics, Physics
  • Letters in Mathematical Physics
  • We construct N-complexes of noncompletely antisymmetric irreducible tensor fields on ℝD, thereby generalizing the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge fields. Although, for N ⩾ 3, the generalized cohomology of these N-complexes is nontrivial, we give a generalization of the Poincaré lemma. Several results which have appeared in various contexts are shown to be particular cases of this generalized Poincaré lemma. 

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