Timeline for Complex torus, C^n/Λ versus (C*)^n
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 17, 2019 at 10:44 | comment | added | LSpice | Yep! Although I just note here in the comments—no need to edit—that the non-compact tori you're defining aren't the same as the real points of the tori in a linear Lie group (which would be the disconnected groups that you wrote down initially). | |
| Jul 17, 2019 at 9:04 | comment | added | Bugs Bunny | Agree! Is it better now? | |
| Jul 17, 2019 at 9:03 | history | edited | Bugs Bunny | CC BY-SA 4.0 |
added 6 characters in body
|
| Jul 17, 2019 at 2:01 | comment | added | LSpice | The torus $\mathbb C^\times$ can occur in a real Lie group, but it is not of the form you quote. (In fact your definition of torus seems strange, since, according to it, all non-compact tori are disconnected.) Perhaps you are thinking algebraically, so that the torus is really $\operatorname{GL}_1^n \times \ker(\operatorname{Res}_{\mathbb C/\mathbb R}\operatorname{GL}_1 \to \operatorname{GL}_1)^m$; but then again $\mathbb C^\times$, or rather $\operatorname{Res}_{\mathbb C/\mathbb R} \operatorname{GL}_1$, is not of this form (it is a quotient). | |
| Jul 16, 2019 at 15:53 | history | answered | Bugs Bunny | CC BY-SA 4.0 |