Leibniz algebroid associated with a Nambu-Poisson structure
نویسندگان
چکیده
منابع مشابه
Leibniz algebroid associated with a Nambu - Poisson structure
The notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact permits to define the modular class of a Nambu-Poisson manifold as an appropiate cohomology class, extending the well-known modular class of Poisson manifolds.
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We show that we can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, a n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and a n-ary version of the Jacobi identity must be skew-symmetric. A similar result holds for a non-antisymmetric version of Lie algebroids.
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Recently it was proposed that the Bagger-Lambert-Gustavsson theory with Nambu-Poisson structure describes an M5-brane in a three-form flux background. In this paper we investigate the superalgebra associated with this theory. We derive the central charges corresponding to M5-brane solitons in 3-form backgrounds. We also show that double dimensional reduction of the superalgebra gives rise to a ...
متن کاملDuality and modular class of a Nambu-Poisson structure
In this paper we introduce cohomology and homology theories for NambuPoisson manifolds. Also we study the relation between the existence of a duality for these theories and the vanishing of a particular Nambu-Poisson cohomology class, the modular class. The case of a regular Nambu-Poisson structure and some singular examples are discussed. Mathematics Subject Classification (2000): 53C15, 53D05...
متن کاملNambu-Poisson manifolds and associated n-ary Lie algebroids
We introduce an n-ary Lie algebroid canonically associated to a NambuPoisson manifold. We also prove that every Nambu-Poisson bracket defined on functions is induced by some differential operator on the exterior algebra, and characterize such operators. Some physical examples are presented.
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1999
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/32/46/310