论文标题
lie $ n $ -algebroids的模块和表示形式
Modules and representations up to homotopy of Lie $n$-algebroids
论文作者
论文摘要
本文研究了差异分级模块和表示为lie $ n $ -Algebroids的同型，对于一般$ n \ in \ mathbb {n} $。描述了伴随和共同连接模块，并解释了伴随的相应拆分版本，并解释了与同型之前的共同连接表示。特别是，详细分析了谎言2-晶格的情况。泊松支架与Lie $ n $ n $ -salgebroid的同源矢量场的兼容性相当于从共同聚合模块到邻接模块的形态，从而导致了较高泊松结构的非限制性的替代表征。此外，根据分组明确计算了一个lie $ n $ algebroid的Weil代数，并且使用lie $ n $ algebroids的表示形式用于编码Double Double Double Doble Doble Dodector Bundles上的分解vb-lie $ n $ n $ n $ n $ n $ n $ -algebroid结构。
This paper studies differential graded modules and representations up to homotopy of Lie $n$-algebroids, for general $n\in\mathbb{N}$. The adjoint and coadjoint modules are described, and the corresponding split versions of the adjoint and coadjoint representations up to homotopy are explained. In particular, the case of Lie 2-algebroids is analysed in detail. The compatibility of a Poisson bracket with the homological vector field of a Lie $n$-algebroid is shown to be equivalent to a morphism from the coadjoint module to the adjoint module, leading to an alternative characterisation of non-degeneracy of higher Poisson structures. Moreover, the Weil algebra of a Lie $n$-algebroid is computed explicitly in terms of splittings, and representations up to homotopy of Lie $n$-algebroids are used to encode decomposed VB-Lie $n$-algebroid structures on double vector bundles.
