论文标题
cartan子组的结构
The Structure of Cartan Subgroups in Lie Groups
论文作者
论文摘要
我们研究了连接的谎言组中的cartan子组的特性和结构。我们获得了Cartan子组的表征，该曲目将Wüstner的结构定理概括为相同。我们表明，卡坦亚组与自由基最大紧凑型亚组的中心化相同。此外，我们描述了一种构造包含某些Nilpotent亚组的Cartan亚组的配方。我们将商组模型中的cartan子组表征为封闭的正常亚组，为环境组中cartan子组的图像。我们还研究了连接的谎言组上功率图的图像的密度，并表明，如果$ k $ Th的功率图的图像限制到封闭的正常亚组，并且商组上的相应映射具有密集的图像，则具有密集的图像。
We study properties and the structure of Cartan subgroups in a connected Lie group. We obtain a characterisation of Cartan subgroups which generalises Wüstner's structure theorem for the same. We show that Cartan subgroups are same as those of the centralizers of maximal compact subgroups of the radical. Moreover, we describe a recipe for constructing Cartan subgroups containing certain nilpotent subgroups in a connected solvable Lie group. We characterise the Cartan subgroups in the quotient group modulo a closed normal subgroup as the images of the Cartan subgroups in the ambient group. We also study the density of the images of power maps on a connected Lie group and show that the image of any $k$-th power map has dense image if its restriction to a closed normal subgroup and the corresponding map on the quotient group have dense images.
