dorsal/arxiv
View SchemaThe local structure of n-Poisson and n-Jacobi manifolds
| Authors | G. Marmo, G. Vilasi, A. Vinogradov |
|---|---|
| Categories | |
| ArXiv ID | physics/9709046 |
| URL | https://arxiv.org/abs/physics/9709046 |
| DOI | 10.1016/S0393-0440(97)00057-0 |
| Journal | J.Geom.Phys.25:141-182,1998 |
Abstract
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.
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"abstract": "N-Lie algebra structures on smooth function algebras given by means of\nmulti-differential operators, are studied. Necessary and sufficient conditions\nfor the sum and the wedge product of two $n$-Poisson sructures to be again a\nmulti-Poisson are found. It is proven that the canonical $n$-vector on the dual\nof an n-Lie algebra g is n-Poisson iff dim(g) are not greater than n+1. The\nproblem of compatibility of two n-Lie algebra structures is analyzed and the\ncompatibility relations connecting hereditary structures of a given n-Lie\nalgebra are obtained. (n+1)-dimensional n-Lie algebras are classified and their\n\"elementary particle-like\" structure is discovered. Some simple applications to\ndynamics are discussed.",
"arxiv_id": "physics/9709046",
"authors": [
"G. Marmo",
"G. Vilasi",
"A. Vinogradov"
],
"categories": [
"math-ph",
"math.MP"
],
"doi": "10.1016/S0393-0440(97)00057-0",
"journal_ref": "J.Geom.Phys.25:141-182,1998",
"title": "The local structure of n-Poisson and n-Jacobi manifolds",
"url": "https://arxiv.org/abs/physics/9709046"
},
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