n-Lie algebra structures on smooth function algebras given by means of multi-differential operators, are studied and their canonical forms are obtained. Necessary and sufficient conditions for the sum and the wedge product of two n-Poisson structures 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 less-than-or-equals, slant 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)-dimensionaln-Lie algebras are classified and their “elementary particle-like” structure is discovered. Some simple applications to dynamics are discussed.

n-Poisson and n-Jacobi Manifolds

MARMO, Giuseppe;VILASI, Gaetano;VINOGRADOV, Alexandre
1998-01-01

Abstract

n-Lie algebra structures on smooth function algebras given by means of multi-differential operators, are studied and their canonical forms are obtained. Necessary and sufficient conditions for the sum and the wedge product of two n-Poisson structures 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 less-than-or-equals, slant 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)-dimensionaln-Lie algebras are classified and their “elementary particle-like” structure is discovered. Some simple applications to dynamics are discussed.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/3017652
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 58
  • ???jsp.display-item.citation.isi??? 59
social impact