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Here is an example from MO illustrating the phenomenon that posts answering questions are being deleted by socalled "non experts". The asker asks for a "non trivial" example of an $A$-Lie algebra.

Vector bundle with a Lie algebra structure

"This post is hidden. It was deleted 2 hours ago by Qiaochu Yuan, Stanley Yao Xiao♦.

Q:"Let V be a "Lie vector bundle", which I define as follows: A Lie vector bundle with a Lie bracket [⋅,⋅] on sections of V, turning it into a Lie algebra and that satisfies [fv,w]=f[v,w] for every local scalar-valued function f and local sections v,w. My question is: are there any other non-trivial examples?"

A: Let $ϕ:L1→L$ be a map of $A/k$-Lie-Rinehart algebras. It follows the kernel $W:=ker(ϕ)$ has an $A$-bilinear bracket $[,]$ and $(W,[,])$ is an $A$-Lie algebra. Hence these objects arise naturally when you study extensions of Lie-Rinehart algebras and cohomology. If $E$ is any $A$-module it follows $End_A(E)$ has a canonical bracket $[,]$ and $(End_A(E),[,])$ is an $A$-Lie algebra. In particular for any finite rank projective module $E$ (a finite rank vector bundle on $Spec(A)$) you get a non trivial example of such.

Given any finite rank projective $A$-module $E$ with $A$ a commutative $k$-algebra, let $At(E)$ be the set of pairs $(x,∇(x))$ with $x∈Der_k(A),∇(x)∈End_k(E)$ with $∇(x)(ae)=a∇(x)(e)+x(a)e$ for $a∈A,e∈E$. There is a canonical projection map

$$π:At(E)→Der_k(A)$$

and $ker(π)≅End_A(E)$. The pair $(At(E),π)$ is an $A/k$-Lie-Rinehart algebra (or a "Lie algebroid"). Hence for any $E$ you may insert $End_A(E)$ into such a sequence.

Share Cite Edit Undelete Flag edited 3 hours ago answered 8 hours ago hm2020's user avatar hm2020

"Is this ChatGPT stuff? It has not much to do with the question. – abx Commented 2 hours ago"

Note: The "moderator" Xiao has not demonstrated much knowledge about this subject as you can see from his performance on MO. In fact he has not answered one single question in the field Lie algebras/algebroids or representation theory. I also get some reponse from "abx" that some students/researhcers may find "abusive". This is a site frequented by students - do we want this type of "abusive" behaviour? Shouldnt the forum/site be more welcoming?

https://math.meta.stackexchange.com/questions/39353/about-deletions-of-answers-outside-of-ones-field

In may I made the following suggestion at MSE:

"@lulu - A user should only be allowed to delete questions/answers in fields where the user has "made significant contributions". Again, it is not clear how to determine what this means, but the principle that a user with enouch "points" can delete any question/answer seems not to be a good principle in my opinion. – hm2020 Commented May 27 at 10:15"

I want once more to suggest this.

"@hm2020 you might consider editing your question to include that as I doubt people here are going to look through your activity on other sites to find such information. That being said, this suggestion would expect people to work against their own self-interest so I'm not sure it's actually very good. – postmortes Commented 48 mins ago"

@postmortes - At MSE I suggested that only users that have "scored points" in a field (maybe more than 300 points) should be able to delete/edit questions/answers in "that field". I repeat this suggestion here. – hm2020 Commented 1 hour ago

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  • $\begingroup$ Here is a link to the comment quoted in the post: math.meta.stackexchange.com/posts/comments/178031 $\endgroup$ Commented Aug 7 at 12:59
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    $\begingroup$ Please note that math.SE and MathOverflow are independent sites and have different community norms, standards and practices. You can't "once more suggest this" on MO if it hasn't been raised before here. Pointing to math.meta.SE is not helpful, except that I note the answer there from Hank Scorpio gives good reasons to not adopt the suggestions. $\endgroup$ Commented Aug 8 at 2:47
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    $\begingroup$ Related: Reviewing questions outside one's expertise $\endgroup$ Commented Aug 8 at 4:02
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    $\begingroup$ Additionally, if a user asks a question on, say, analytic number theory (an area in which I have no questions or answers on MO) but it is clearly a crank question, or very obviously generated by an LLM, then as a research mathematician who can spot patent nonsense when I see it, I should be able to close said question. $\endgroup$ Commented Aug 8 at 6:37
  • $\begingroup$ @DavidRoberts - the problem is - as in this case - when users and moderators "apply this principle" to post "abusive posts" - this must be avoided. $\endgroup$ Commented Aug 8 at 10:33
  • $\begingroup$ @DavidRoberts - I do not agree with the answer given at your link - If the MSE and MO-sites are going to "make a contribution to academia" this problem has to be solved. If you want to delete/edit a question on one of these sites, you must first prove your capability in the field. $\endgroup$ Commented Aug 8 at 13:01
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    $\begingroup$ @hm2020 both MO and MSE have been around for over fifteen years. That they have 'made a contribution to academia' is factually uncontestable, though I'm sure there are differing opinions as to the nature and quality of that contribution. Perhaps more importantly though, you haven't indicated how the site is supposed to know a user's particular facility in an area, and without that you're just complaining. $\endgroup$ Commented Aug 8 at 13:19
  • $\begingroup$ @postmortes - At MSE I suggested that only users that have "scored points" in a field (maybe more than 300 points) should be able to delete/edit questions/answers in "that field". I repeat this suggestion here. $\endgroup$ Commented Aug 19 at 12:41
  • $\begingroup$ @hm2020 you might consider editing your question to include that as I doubt people here are going to look through your activity on other sites to find such information. That being said, this suggestion would expect people to work against their own self-interest so I'm not sure it's actually very good. $\endgroup$ Commented Aug 19 at 13:28

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There are only so many moderators, and the field of mathematics as a whole is too big to demand that every speciality has an expert that is a moderator, and only those experts are allowed to make judgements and act on particular answer, question or comment. I don't have to be an expert in French pastry baking to know when I've bought a stale croissant. Likewise, an editor can make judgements on posts outside their area of expertise when it is clear from context and other clues what might need doing. If a user asks a question on, say, analytic number theory (an area in which I have no questions or answers on MO) but it is clearly a crank question, or very obviously generated by an LLM, then as a research mathematician who can spot patent nonsense when I see it, I should be able to close said question.

However, mods are not infallible, and that is why we have the post Requests for reopen and undelete votes for closed and deleted questions in case something gets deleted (or closed) and it can be undeleted (or reopened) — and I would include answers here as well as questions. Additionally, there is an 'undelete' button under your answer, and this would place the answer in a review queue, for high-rep users to have a look at and make their own mind up.

For the purposes of getting the record straight, the comment on your question queried the source of the answer, and another user also voted to delete, this was not a unilateral action by a moderator, though a moderator's close or delete vote has more weight than a generic user's.

The rest of your question referring to matters on math.SE is not relevant for MathOverflow, because are independent sites and have different community norms, standards and practices.

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  • $\begingroup$ "The rest of your question referring to matters on math.SE is not relevant for MathOverflow, because are independent sites and have different community norms, standards and practices." The two sites are frequented by people from the same community - the "mathematics community" and the same rules should apply to both sites in my opinion. $\endgroup$ Commented Aug 19 at 10:52
  • $\begingroup$ In fact if you look at the two sites' "conde of conduct" at math.stackexchange.com/conduct and mathoverflow.net/conduct they look very much the same. $\endgroup$ Commented Aug 19 at 10:53
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    $\begingroup$ The code of conduct is a generic Stack Exchange thing. Go look at more sites. That doesn't mean MO should have the same community norms as eg parenting.SE or writing.SE $\endgroup$ Commented Aug 19 at 11:39
  • $\begingroup$ you mention that MO and MSE have "different community norms" - where are the MO norms written down? $\endgroup$ Commented Aug 19 at 13:03
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    $\begingroup$ They are not, because they aren't legally binding terms. Please, instead of debating with me, put a request at meta.mathoverflow.net/questions/223/… for undeletion $\endgroup$ Commented Aug 19 at 21:04

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