The local structure of n-Poisson and n-Jacobi manifolds

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dc.creatorMarmo, G.
dc.creatorVilasi, G.
dc.creatorVinogradov, A.
dc.date1997-09-30
dc.date.accessioned2026-07-07T10:34:40Z
dc.date.available2026-07-07T10:34:40Z
dc.descriptionN-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.
dc.description45 pages, latex, no figures
dc.identifierhttps://arxiv.org/abs/physics/9709046
dc.identifierhttp://arxiv.org/abs/physics/9709046
dc.identifierJ.Geom.Phys.25:141-182,1998
dc.identifierdoi:10.1016/S0393-0440(97)00057-0
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/179553
dc.subjectMathematical Physics
dc.titleThe local structure of n-Poisson and n-Jacobi manifolds
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