Timeline for Generating sets for $\mathrm{SU}(1,1;\mathcal{O}_K)$ or $\mathrm{PU}(1,1;\mathcal{O}_K)$?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 21, 2016 at 17:34 | comment | added | Joe Wells | @JeanRaimbault I just noticed your first comment - can you expand upon it a bit? If the two groups are isomorphic (at least, I believe that's what the first sentence in the answer is saying), shouldn't generators for one group map to generators for the other? | |
| Nov 20, 2016 at 12:27 | comment | added | Joe Wells | Thank you so much for this very thorough answer. I have some reading to do. | |
| Nov 20, 2016 at 12:26 | vote | accept | Joe Wells | ||
| Nov 20, 2016 at 9:52 | comment | added | Jean Raimbault | By the way, I don't know what you mean by "wide open" but Swan's algorithm gives a complete solution to finding a finite generating set of a Bianchi group. It's been implemented in Pari by Rahm maths.nuigalway.ie/~rahm/MathematicalSoftware.htm, there is also another algorithm for all arithmetic Kleinian groups in Magma by Page: normalesup.org/~page/Recherche/Logiciels/logiciels-en.html | |
| Nov 20, 2016 at 9:46 | comment | added | Jean Raimbault | (1,1)-hermitian forms over $\mathcal O_K$ "parametrise" totally geodesic surfaces in the Bianchi orbifolds, so knowing generators for the latter is not helpful for the original question. | |
| Nov 19, 2016 at 21:56 | history | edited | john mangual | CC BY-SA 3.0 |
link to Ford
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| Nov 19, 2016 at 21:32 | history | answered | john mangual | CC BY-SA 3.0 |