Timeline for Action of $\mathbb C^*$ on a closed orbit of a torus

9 events

when toggle format	what		by	license	comment
Mar 10, 2016 at 12:37	vote	accept	cll
Mar 1, 2016 at 19:00	comment	added	Ariyan Javanpeykar		@JasonStarr Thank you for the explanation. Shame on me. smiley face
Mar 1, 2016 at 16:11	comment	added	Jason Starr		@AriyanJavanpeykar. Define $y=\lambda(x-1)+1$. Then $\mu\ast y$ equals $\mu(y-1)+1$. But $y-1$ equals $\lambda(x-1)$. Thus $\mu\ast y$ equals $\mu\lambda(x-1)+1$. So $\mu\ast(\lambda\ast x)$ equals $(\mu\lambda)\ast x$. smiley face
Mar 1, 2016 at 15:35	answer	added	Thomas		timeline score: 3
Mar 1, 2016 at 15:12	comment	added	Ariyan Javanpeykar		@JasonStarr Is your second action really an action? It seems to me that $(\lambda \cdot \mu) \ast x \neq \lambda \ast (\mu\ast x)$
Mar 1, 2016 at 14:36	answer	added	Jason Starr		timeline score: 4
Mar 1, 2016 at 14:29	comment	added	Jason Starr		No. Consider the "standard" action of $\mathbb{C}^$ on $\mathbb{A}^1$ by $\lambda\cdot x= \lambda x$, and also the second action of $\mathbb{C}^$ on $\mathbb{A}^1$ by $\lambda \ast x = \lambda(x-1)+1$.
Mar 1, 2016 at 14:24	review	First posts
Mar 1, 2016 at 15:02
Mar 1, 2016 at 14:22	history	asked	cll	CC BY-SA 3.0