论文标题
关于奇异叶的对称性
On symmetries of singular foliations
论文作者
论文摘要
本文表明，单个叶子$ \ mathcal f $在单一叶子上的弱对称作用薄弱的对称性动作诱导了$ \ mathfrak {g mathfrak {g} $ to dglla of vorce of forcector $ \ nmart $ \ nmart $ $ \ f的dgla dgla from $ \ mathfrak {g} $ to $ \ mathfrak {g} $的唯一唯一的对称性动作。 R. Mehta和M. Zambon研究的这样的谎言$ \ infty $ -MORPHISMWAS为$ l_ \ infty $ -Algebra Action。我们从这一总体结果中得出几种几何后果。例如，我们举例说明了对仿射子变量的谎言代数作用，该动作无法扩展在环境空间上。最后，我们介绍了双向塔塔的概念，并向这些叶子介绍了对称性的概念。
This paper shows that a weak symmetry action of a Lie algebra $\mathfrak{g}$ on a singular foliation $\mathcal F$ induces a unique up to homotopy Lie$\infty$-morphism from $\mathfrak{g}$ to the DGLA of vector fields on a universal Lie $\infty$-algebroid of $\mathcal F$. Such a Lie $\infty$-morphismwas studied by R. Mehta and M. Zambon as $L_\infty$-algebra action. We deduce from this general result several geometrical consequences. For instance, we give an example of a Lie algebra action on an affine sub-variety which cannot be extended on the ambient space. Last, we introduce the notion of bi-submersion towers over a singular foliation and lift symmetries to those.
