论文标题
断开的真实代数组的电源图的密集图像
Dense images of the power maps for a disconnected real algebraic group
论文作者
论文摘要
令$ g $为一个复杂的代数组，该组定义在$ \ mathbb r $上，这不一定是Zariski连接的。在本文中，我们研究了Power Maps $ g \ to G^k $，$ k \ in \ Mathbb n $的图像的密度，在$ g $的真实点上，即配备了具有真实拓扑的$ g（\ Mathbb R）$。结果，我们将P. Chatterjee的定理扩展了$ G（\ Mathbb R）$的半元素元素的电源图的溢流性。我们还表征了断开的组$ G（\ Mathbb R）$的电源图的溢流力。结果特别用于描述$ g（\ Mathbb r）的指数映射的图像。$。
Let $G$ be a complex algebraic group defined over $\mathbb R$, which is not necessarily Zariski connected. In this article, we study the density of the images of the power maps $g\to g^k$, $k\in\mathbb N$, on real points of $G$, i.e., $G(\mathbb R)$ equipped with the real topology. As a result, we extend a theorem of P. Chatterjee on surjectivity of the power map for the set of semisimple elements of $G(\mathbb R)$. We also characterize surjectivity of the power map for a disconnected group $G(\mathbb R)$. The results are applied in particular to describe the image of the exponential map of $G(\mathbb R).$
