The local structure of n-Poisson and n-Jacobi manifolds
Marmo, G. ; Vilasi, G. ; Vinogradov, A.
arXiv, 9709046 / Harvested from arXiv
Text on arXiv
N-Lie algebra structures on smooth function algebras given by means of multi-differential operators, are studied. Necessary and sufficient conditions for the sum and the wedge product of two $n$-Poisson sructures to be again a multi-Poisson are found. It is proven that the canonical $n$-vector on the dual of an n-Lie algebra g is n-Poisson iff dim(g) are not greater than n+1. The problem of compatibility of two n-Lie algebra structures is analyzed and the compatibility relations connecting hereditary structures of a given n-Lie algebra are obtained. (n+1)-dimensional n-Lie algebras are classified and their "elementary particle-like" structure is discovered. Some simple applications to dynamics are discussed.
Publié le : 1997-09-30
Classification:  Mathematical Physics 
@article{9709046,
     author = {Marmo, G. and Vilasi, G. and Vinogradov, A.},
     title = {The local structure of n-Poisson and n-Jacobi manifolds},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9709046}
}

Marmo, G.; Vilasi, G.; Vinogradov, A. The local structure of n-Poisson and n-Jacobi manifolds. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9709046/