OF MULTIPLICATIVE DIRAC STRUCTURES
OF MULTIPLICATIVE DIRAC STRUCTURES
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发表时间：
2013
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通讯作者：
P. Wamba;A. Ntyam
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文献类型：
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作者：
P. Wamba;A. Ntyam
Dirac结构的高阶切提升和一些性质已在[9]中定义，并在[11]中研究。文[10]用同样的方法研究了高阶Poisson结构的切提升，并给出了一些应用。特别是，作者研究了李代数胚的性质和奇异foliations引起这些提升。本文研究了乘性Poisson结构、乘性Dirac结构的高阶切提升，并描述了由这些切提升诱导的李双代数体结构和代数体-Dirac结构。引言我们表示LG和LA的李群胚和李代数胚的类别，分别。存在一个自然函子A：LG → LA，它将每个对象G ∈ LG映射到对象AG ∈ LA，并且李群胚φ：G1 → G2的每个态射映射到李代数胚态射Aφ：AG 1 → AG 2。它被称为李函子并保持乘积丛。设G是流形M上的李群胚，我们用G（2）表示可合成群胚对的集合，我们记得，Poisson群胚是一对（G;其中，G是G上的Poisson结构，在乘法映射Λ = {（g，h，gh），（g，h）∈ G（2）}是G×G×G的上迷向子流形，其中G表示G具有相反的Poisson结构.我们说，双向量G是一个乘法双向量。另一方面，众所周知，李双代数胚是2010年数学学科分类：小学53 C15;中学53 C75，53 D 05。
The tangent lifts of higher order of Dirac structures and some properties have been defined in [9] and studied in [11]. By the same way, the tangent lifts of higher order of Poisson structures have been studied in [10] and some applications are given. In particular, the authors have studied the nature of the Lie algebroids and singular foliations induced by these lifting. In this paper, we study the tangent lifts of higher order of multiplicative Poisson structures, multiplicative Dirac structures and we describe the Lie bialgebroid structures and the algebroid-Dirac structures induced by these prolongations. Introduction We denote by LG and LA the categories of Lie groupoids and Lie algebroids, respectively. There is a natural functor A : LG → LA, which maps each object G ∈ LG to the object AG ∈ LA, and every morphism of Lie groupoids φ : G1 → G2 is mapped to the Lie algebroid morphism Aφ : AG1 → AG2. It is called the Lie functor and preserves the product bundles. Let G be a Lie groupoid over a manifold M , we denote by G(2) the set of composable groupoid pairs and we recall that, a Poisson groupoid is a pair (G; ΠG) where ΠG is a Poisson structure on G which is multiplicative in the sense that the graph of the multiplication map Λ = { (g, h, gh) , (g, h) ∈ G(2) } is a coisotropic submanifold of G×G×G , where G means that G is equipped with the opposite Poisson structure. We say that the bivector ΠG is a multiplicative bivector. On the other hand, it is well known that Lie bialgebroid is a 2010 Mathematics Subject Classification: primary 53C15; secondary 53C75, 53D05.