Timeline for Zariski density for certain subsemigroups
Current License: CC BY-SA 4.0
20 events
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| Jul 9, 2021 at 17:08 | history | edited | Zestylemonzi | CC BY-SA 4.0 |
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| S May 30, 2021 at 19:01 | history | bounty ended | CommunityBot | ||
| S May 30, 2021 at 19:01 | history | notice removed | CommunityBot | ||
| S May 22, 2021 at 17:39 | history | bounty started | Zestylemonzi | ||
| S May 22, 2021 at 17:39 | history | notice added | Zestylemonzi | Draw attention | |
| May 21, 2021 at 14:50 | comment | added | Zestylemonzi | @rpotrie, you're right, I'd like that $0 < \delta < \infty$. | |
| May 21, 2021 at 0:28 | comment | added | rpotrie | I don't know, but if your group is not discrete then the series never converges, so perhaps you can make some counterexample that way. I think you should ask that the group $\Gamma$ is discrete, right? | |
| May 20, 2021 at 22:02 | comment | added | Zestylemonzi | Thanks for the comments. @YCor, it came up whilst reading about counting problems related to certain representations into GL(d,R). @rpotrie, thanks for the reference - do we know that we can associate a `nice action' to a subgroup of GL(d,R) so that the norm function behaves like displacement? | |
| May 20, 2021 at 21:40 | comment | added | rpotrie | arxiv.org/abs/1411.6817 may be useful? | |
| May 20, 2021 at 21:19 | comment | added | YCor | Where did the question occur? | |
| May 20, 2021 at 21:18 | comment | added | YCor | Eventually if $\Lambda$ is the subgroup generated by $N$, then $\sum_{x\in\Lambda}e^{-\delta\|x\|}=\infty$. Hence, it is no restriction to assume that $N$ is a subgroup. | |
| May 20, 2021 at 17:06 | history | edited | YCor | CC BY-SA 4.0 |
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| May 20, 2021 at 16:29 | history | edited | Zestylemonzi | CC BY-SA 4.0 |
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| May 20, 2021 at 16:27 | comment | added | Benjamin Steinberg | Actually reading the comments to my answer a Zariski closed submonoid M of GL_n is a subgroup just because any closed subspace is Noetherian and a direct algebraic argument | |
| May 20, 2021 at 16:26 | comment | added | Zestylemonzi | Thanks for the comment - I'll add a reference to this in the question. | |
| May 20, 2021 at 16:22 | comment | added | Benjamin Steinberg | In more detail, my answer to mathoverflow.net/questions/246974/… shows the Zariski closure of a subsemigroup is a group over an algebraically closed field using Ax-Grothendieck. But this is also valid over R by Białynicki-Birula, A., Rosenlicht, M.: Injective Morphisms of Real Algebraic Varieties. Maybe there is a more direct argument to deduce or from the complex case | |
| May 20, 2021 at 16:17 | history | edited | Zestylemonzi | CC BY-SA 4.0 |
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| May 20, 2021 at 16:17 | comment | added | Benjamin Steinberg | The inverse of an element is in its Zariski closure so this is equivalent to whether the group generated by N is Zariski dense. | |
| May 20, 2021 at 16:17 | history | edited | Zestylemonzi | CC BY-SA 4.0 |
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| May 20, 2021 at 15:56 | history | asked | Zestylemonzi | CC BY-SA 4.0 |