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