Timeline for Are there algorithms for deciding or solving conjugacy in integer quaternion rings?
Current License: CC BY-SA 4.0
29 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 13, 2020 at 21:33 | history | edited | user157838 | CC BY-SA 4.0 |
deleted 1563 characters in body
|
| May 13, 2020 at 21:32 | comment | added | user157838 | @AlexM. I have removed that source | |
| May 13, 2020 at 16:36 | comment | added | Alex M. | @user157838: No, Hindawi is not ok. Their peer reviewing process is... "problematic", to say the least. I constantly find emails from them in my "spam" folder, in which they promise very quick acceptance for publication. Such aggressive self-promotion should be condemned; and the promise of such quick reviewing tells a lot about its quality. Regarding the authors' English, I simply cannot understand the quoted paragraph "Regarding this [...] predicted groups": it simply makes no sense in English. Anyway, your question was about something else, so let us end this off-topic discussion here. | |
| May 13, 2020 at 14:35 | comment | added | user157838 | @AlexM. Is Hindawi considered a reputable publisher? I looked into it briefly and found they were generally considered to be ok. Furthermore, I didn't want to discard a paper solely because of the English. | |
| May 13, 2020 at 9:10 | comment | added | Alex M. | @user157838: Just a side note: you cite some authors, but their English is so bad, that I wouldn't even bother reading their papers. But then, they got published by Hindawi, so... this should tell a lot. | |
| May 12, 2020 at 22:19 | comment | added | Lev Soukhanov | I'm currently reading arxiv.org/pdf/1709.02079.pdf this, hopefully it is related. As @AchimKrause points out, currently the problem is still trivial because considered over Q. You should probably work with polynomials over H (similar to standard NTRU) to obtain interesting lattice problem. | |
| May 12, 2020 at 17:40 | comment | added | Achim Krause | If I am not mistaken, the question as written now follows by doing the linear algebra approach over $\mathbb{Q}$ and then scaling $z$ to get integer coefficients. | |
| S May 12, 2020 at 17:24 | history | suggested | Steven Stadnicki | CC BY-SA 4.0 |
Small further revision, cleaning up problem statements in line with a previous comment and closing a dangling parenthetical expression I left.
|
| May 12, 2020 at 17:23 | review | Suggested edits | |||
| S May 12, 2020 at 17:24 | |||||
| S May 12, 2020 at 17:03 | history | suggested | Steven Stadnicki | CC BY-SA 4.0 |
Cleared up the first paragraph
|
| May 12, 2020 at 16:49 | review | Suggested edits | |||
| S May 12, 2020 at 17:03 | |||||
| May 12, 2020 at 16:43 | comment | added | user157838 | @LevSoukhanov Not exactly, I am just interested in the applicability of a quaternion ring to non-commutative crypto. | |
| May 12, 2020 at 13:26 | comment | added | Lev Soukhanov | Excuse me, I would like you to clarify something. I've looked up few papers on this theme. Is it some non-commutative version of NTRU? | |
| May 12, 2020 at 12:25 | history | edited | user157838 | CC BY-SA 4.0 |
deleted 1 character in body
|
| May 12, 2020 at 12:23 | comment | added | user157838 | @StevenStadnicki I think you are right, I do mean conjugacy in rings, and I realize now that my question was not formulated correctly. I apologize, I am still very shaky with this kind of math. I will edit the question to be more specific | |
| May 11, 2020 at 23:21 | comment | added | John Voight | @user157838: yes, the linear algebra approach works in the unit group of any quaternion algebra over a (computable) field. | |
| May 11, 2020 at 20:26 | comment | added | Steven Stadnicki | Presuming that the question here is about conjugacy in these rings, then the problem is likely to be Complicated, by analogy with similar problems in $SL_2(\mathbb{Z})$ for instance. I think there's an interesting question here but you need to be more specific about it. | |
| May 11, 2020 at 20:25 | comment | added | Steven Stadnicki | (Also, if you do mean 'as a group' then the problem is trivial, because the group structure on Hurwitz or Lipschitz quaternions is the additive one, which is still commutative.) | |
| May 11, 2020 at 20:24 | comment | added | Steven Stadnicki | When you say 'the group' do you mean 'the ring'? Neither the Hurwitz nor Lipschitz quaternions form a field, so you have to be very careful using expressions like $z^{-1}$ in such a case. The question of whether there's a $z$ such that $zy=xz$ is very different from the question of whether there's an invertible such $z$ (which is nearly trivial; very few Hurwitz or Lipschitz quaternions are invertible multiplicatively, after all...) | |
| May 11, 2020 at 18:05 | comment | added | LSpice | I removed the irrelevant [algebraic-groups] and [free-groups] tags. | |
| May 11, 2020 at 18:03 | history | edited | LSpice | CC BY-SA 4.0 |
Names of papers; removed irrelevant [algebraic-groups] and [free-groups] tags
|
| May 11, 2020 at 17:23 | history | edited | user157838 | CC BY-SA 4.0 |
added 69 characters in body
|
| May 10, 2020 at 22:14 | comment | added | user157838 | @JohnVoight Is that true for all quaternion groups, like the Lipschitz or Hurwitz? | |
| May 10, 2020 at 20:05 | comment | added | John Voight | mathoverflow.net/questions/358830/… | |
| May 10, 2020 at 19:25 | review | Close votes | |||
| May 14, 2020 at 2:58 | |||||
| May 10, 2020 at 19:18 | answer | added | Vít Tuček | timeline score: 4 | |
| May 10, 2020 at 19:01 | comment | added | Watson Ladd | I'm going to assume you are discussing the quaternions over $\mathbb{R}$. In this case what you are asking is essentially the conjugacy structure of $\mathrm{SO}(3)$, and it's easiest to see geometrically. Every rotation in three dimensions is a rotation by some angle around an axis, and two rotations by the same angle are conjugate via any rotation that takes one axis to the to other. The structure of the double cover doesn't change much about the conjugacy. | |
| May 10, 2020 at 15:57 | review | First posts | |||
| May 10, 2020 at 19:38 | |||||
| May 10, 2020 at 15:53 | history | asked | user157838 | CC BY-SA 4.0 |