论文标题
谎言$ \ infty $ -Algebroids和伴随表示形式的模块化类别
Modular class of Lie $\infty$-algebroids and adjoint representation
论文作者
论文摘要
我们研究了$ q $ - manifolds的模块化类别，尤其是否定分级的谎言$ \ infty $ -Algebroid。我们表明了这些类的几个描述的等效性，即它与各种作者引入的类匹配，并且该概念是同质的不变性。在此过程中，拼出了谎言$ \ infty $ -Algebroid的伴随和共同连接动作。我们还明确地写下了一些二元性，例如在与lie $ \ infty $ -Algebroids的同义及其$ Q $ -Manifold等效的表示之间，我们希望将其用于未来参考。
We study the modular class of $Q$-manifolds, and in particular of negatively graded Lie $\infty$-algebroid. We show the equivalence of several descriptions of those classes, that it matches the classes introduced by various authors and that the notion is homotopy invariant. In the process, the adjoint and coadjoint actions up to homotopy of a Lie $\infty$-algebroid are spelled out. We also wrote down explicitly some dualities, e.g. between representations up to homotopies of Lie $\infty$-algebroids and their $Q$-manifold equivalent, which we hope to be of use for future reference.
