论文标题
由与七维可溶性谎言代数相对应的谎言组的通用共同连接轨道形成的叶子
Foliations Formed by Generic Coadjoint Orbits of Lie Groups Corresponding to a Class Seven-Dimensional Solvable Lie Algebras
论文作者
论文摘要
我们考虑所有已连接并简单地连接的7维谎言组，其谎言代数为nilradical $ \ g_ {5,2} = \ s \ {x_1，x_1，x_2，x_3，x_4，x_4，x_5 \ colon [x_1，x_1，x_2]首先，我们对所有被考虑的谎言组的共同连接表示中的最大维轨道进行了几何描述。接下来，我们证明，对于每个被考虑的群体，通用共同连接轨道的家族在Connes的意义上形成了可衡量的叶子。最后，还提供了所有这些叶子的拓扑分类。
We consider all connected and simply connected 7-dimensional Lie groups whose Lie algebras have nilradical $\g_{5,2} = \s \{X_1, X_2, X_3, X_4, X_5 \colon [X_1, X_2] = X_4, [X_1, X_3] = X_5\}$ of Dixmier. First, we give a geometric description of the maximal-dimensional orbits in the coadjoint representation of all considered Lie groups. Next, we prove that, for each considered group, the family of the generic coadjoint orbits forms a measurable foliation in the sense of Connes. Finally, the topological classification of all these foliations is also provided.
