论文标题
li子类固定的横向密度束和模块化类别
The transverse density bundle and modular classes of Lie groupoids
论文作者
论文摘要
在本说明中，我们重新审视了横向密度束的概念以及谎言代数和lie glopoids的模块化类别的概念；特别是，我们指出的是，应该使用横向密度束$ \ Mathcal {d} _ {a}^{\ textrm {tr}} $而不是$ q_a $，这是谈论模块化类时通常使用的表示。这样做的原因之一是，正如我们将看到的那样，$ q_a $并不是与lie groupoid提出的堆栈相关的对象（通常，它不是groupoid的表示！）。
In this note we revisit the notions of transverse density bundle and of modular classes of Lie algebroids and Lie groupoids; in particular, we point out that one should use the transverse density bundle $\mathcal{D}_{A}^{\textrm{tr}}$ instead of $Q_A$, which is the representation that is commonly used when talking about modular classes. One of the reasons for this is that, as we will see, $Q_A$ is not really an object associated to the stack presented by a Lie groupoid (in general, it is not a representation of the groupoid!).
