Leibniz algebroid associated with a Nambu-Poisson structure

Abstract

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.

References in corpus (4)

• The local structure of n-Poisson and n-Jacobi manifolds
• Remarks on Nambu-Poisson and Nambu-Jacobi brackets
• Nambu mechanics, $n$-ary operations and their quantization
• On Filippov algebroids and multiplicative Nambu-Poisson structures

Cited by in corpus (24)

• Leibniz algebroids, twistings and exceptional generalized geometry
• Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
• Modular Classes of Loday Algebroids
• On higher analogues of Courant algebroids
• Cup-product for equivariant Leibniz cohomology and zinbiel algebras
• Duality and modular class of a Nambu-Poisson structure
• Nambu-Poisson manifolds and associated n-ary Lie algebroids
• Multi-Dirac Structures and Hamilton-Pontryagin Principles for Lagrange-Dirac Field Theories
• The geometry of Lie algebroids and its applications to optimal control
• Reduction of Nambu-Poisson manifolds by regular distributions
• Omni $n$-Lie algebras and linearization of higher analogues of Courant algebroids
• Homological sections of Lie algebroids
• Lie Algebroids in the Loday-Pirashvili Category
• On split regular Hom-Leibniz-Rinehart algebras
• Multiplicative Nambu structures on Lie groupoids
• Remarks on generalized Lie algebroids and related concepts
• The Free Courant Algebroid
• Courant algebroid lifts and curved Courant algebroids
• Higher derived brackets, strong homotopy associative algebras and Loday pairs
• Higher Lie and Leibniz algebras
• Nambu system associated with n-dimensional maps
• Para-associative Algebroids
• Computations of Nambu-Poisson cohomologies
• Geometry of Membrane Sigma Models