论文标题
乘法联系及其谎言理论
Multiplicative Connections and Their Lie Theory
论文作者
论文摘要
我们定义和研究li子类样的切线束中的乘法连接。乘法连接是线性连接，可满足与群体结构的适当兼容性。我们的定义是自然的，从某种意义上说，当lie groupoid上的线性连接在且仅当它的扭转是bursztyn-drummond [5]意义上的乘法张量时，并且其测量喷雾是乘法矢量场。我们确定了对乘法连接的存在的障碍。我们还讨论了切线捆绑包中的乘法连接的无限版本，我们称之为无限的乘法（IM）连接，我们证明了IM连接的集成定理。最后，我们提出了一些玩具示例。
We define and study multiplicative connections in the tangent bundle of a Lie groupoid. Multiplicative connections are linear connections satisfying an appropriate compatibility with the groupoid structure. Our definition is natural in the sense that a linear connection on a Lie groupoid is multiplicative if and only if its torsion is a multiplicative tensor in the sense of Bursztyn-Drummond [5] and its geodesic spray is a multiplicative vector field. We identify the obstruction to the existence of a multiplicative connection. We also discuss the infinitesimal version of multiplicative connections in the tangent bundle, that we call infinitesimally multiplicative (IM) connections and we prove an integration theorem for IM connections. Finally, we present a few toy examples.
