论文标题
同型泊松代数，Maurer-Cartan元素和Clwx 2-偏源型的狄拉克结构
Homotopy Poisson algebras, Maurer-Cartan elements and Dirac structures of CLWX 2-algebroids
论文作者
论文摘要
在本文中，我们构建了与分裂谎言2-远程相关的3度的同型泊松代数，通过该代数，我们提供了一种新的方法来表征分裂的谎言2-二重子制剂。我们开发了与分裂谎言2-晶状体相关的微积分，并建立了分裂谎言2-晶状体的Manin三重理论。更确切地说，我们给出了严格的狄拉克结构的概念，并定义了分裂谎言2-晶状体的Manin三倍为CLWX 2-Elgebroid，具有两个横向严格的DIRAC结构。我们表明，分裂谎言2-晶格和撒谎的2个双子晶状体之间有一对一的对应关系。我们进一步介绍了CLWX 2-晶格的弱狄拉克结构的概念，并表明同型托管泊松代数的毛勒 - 卡丹元素的图3与分裂的谎言2基因生物相关的2型二重晶状体是弱的狄拉克结构。给出了各种示例，包括弦序2-代数，分裂的2-偏格型构建，这些分布由可集成的分布和左对称代数构建。
In this paper, we construct a homotopy Poisson algebra of degree 3 associated to a split Lie 2-algebroid, by which we give a new approach to characterize a split Lie 2-bialgebroid. We develop the differential calculus associated to a split Lie 2-algebroid and establish the Manin triple theory for split Lie 2-algebroids. More precisely, we give the notion of a strict Dirac structure and define a Manin triple for split Lie 2-algebroids to be a CLWX 2-algebroid with two transversal strict Dirac structures. We show that there is a one-to-one correspondence between Manin triples for split Lie 2-algebroids and split Lie 2-bialgebroids. We further introduce the notion of a weak Dirac structure of a CLWX 2-algebroid and show that the graph of a Maurer-Cartan element of the homotopy Poisson algebra of degree 3 associated to a split Lie 2-bialgebroid is a weak Dirac structure. Various examples including the string Lie 2-algebra, split Lie 2-algebroids constructed from integrable distributions and left-symmetric algebroids are given.
