Timeline for How to construct an explicit isomorphism of the split Quaternion Algebra $(a,b)_F$ over the field $F$ to $\mathrm{Mat}_2(F)$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 23 at 15:17 | comment | added | Samuil Lee | @Aurel Could you please share the proof of this algorithm in the case of rational numbers or maybe articles where it can be seen? Because all the notes that I have seen on this problem are quite unclear and messy | |
| May 22 at 22:28 | history | edited | Aurel | CC BY-SA 4.0 |
latex typo
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| May 22 at 20:13 | comment | added | Aurel | We know a polynomial-time algorithm over $F$ a finite field, over $F=k(t)$ where $k$ is a finite field (and maybe quadratic extensions thereof, I would need to check) for $F$ the rationals or a quadratic field, and an algorithm which is heuristically subexponential for other number fields. Note that in the rationals and quadratic cases, you are supposed to have first suceeded in proving isomorphism before trying to compute an isomorphism, which may require factorisation of some integers (also subexponential time in the worst case). | |
| May 22 at 19:30 | history | edited | Samuil Lee |
edited tags
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| May 22 at 17:55 | comment | added | Samuil Lee | @DieterKadelka Yes on the both questions | |
| May 22 at 17:53 | comment | added | Dieter Kadelka | Please be a little more specific. First, do you mean the paper eprints.sztaki.hu/9729/2/Kutas_73_30340642_ny.pdf ? Second, is $(a,b)_F = H_K(a,b)$ ? | |
| May 22 at 17:41 | history | edited | Samuil Lee | CC BY-SA 4.0 |
added 3 characters in body
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| May 22 at 15:30 | history | edited | YCor | CC BY-SA 4.0 |
fixed English/formatting
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| S May 22 at 15:04 | review | First questions | |||
| May 22 at 15:47 | |||||
| S May 22 at 15:04 | history | asked | Samuil Lee | CC BY-SA 4.0 |