Tensor Fields of Mixed Young Symmetry Typeand NComplexes
Abstract
We construct Ncomplexes of noncompletely 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 Ncomplexes 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 [10].
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2002
 DOI:
 10.1007/s002200200610
 arXiv:
 arXiv:math/0110088
 Bibcode:
 2002CMaPh.226..393D
 Keywords:

 Mathematics  Quantum Algebra;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 47 pages