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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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SP Science China Press

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10.1016/0014-2999(91)90072-x

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1869-1862

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On higher analogues of Courant algebroids

Authors: YanHui Bi YunHe Sheng
Publish Date: 2011/01/14
Volume: 54, Issue: 3, Pages: 437-447
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Abstract

In this paper we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle TM ⊕ ∧ n TM for an mdimensional manifold As an application we revisit NambuPoisson structures and multisymplectic structures We prove that the graph of an n+1vector field π is closed under the higherorder Dorfman bracket iff π is a NambuPoisson structure Consequently there is an induced Leibniz algebroid structure on ∧ n TM The graph of an n+1form ω is closed under the higherorder Dorfman bracket iff ω is a premultisymplectic structure of order n ie dω = 0 Furthermore there is a Lie algebroid structure on the admissible bundle A ⊂ ∧ n TM In particular for a 2plectic structure it induces the Lie 2algebra structure given in Baez Hoffnung and Rogers 2010

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