# User talk:Arcfrk

Hi there. I saw your reply to my expert request on the Artin reciprocity page and I look forward to any insight you might be able to add. Welcome to Wikipedia. You may want to drop by Wikipedia:WikiProject Mathematics and see what other mathematicians are talking about around here. VectorPosse 10:49, 16 March 2007 (UTC)

## Welcome!

Hello, Arcfrk, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or ask your question and then place `{{helpme}}` after the question on your talk page. Again, welcome!

I was also very impressed by your comments on Hilbert space. Welcome indeed! Geometry guy 11:43, 16 March 2007 (UTC)

Welcome from me too. Oleg Alexandrov (talk) 15:33, 16 March 2007 (UTC)
The English-language Wikipedia mathematics community tends to be a blissfully quiet backwater compared to the turbulence of the mainstream. Our articles are numerous, but vary widely in age, thoroughness, accuracy, and so on. Some of our editors are multilingual, but the typical Yank is not. Many of our editors have some level of university training, usually enough to help settle technical disputes. Good help is always appreciated, as is good company. Welcome. --KSmrqT 17:27, 16 March 2007 (UTC)

## Barnstar

 The E=mc² Barnstar On this, my 10,000th edit, I award you this Barnstar for overall excellence of contributions to mathematical articles on Wikipedia. Thank you so much, and keep up the exceptional work. silly rabbit (talk) 22:43, 4 April 2008 (UTC)

## Re: Request for clarification

Which articles are you talking about? I was probably importing old edits from the Nostalgia Wikipedia, so the edit history of the article could contain more edits from 2001. Graham87 07:08, 27 December 2009 (UTC)

## Stanley-Reisner ring

You might be able to make this article more accessible. Charles Matthews (talk) 08:52, 21 March 2010 (UTC)

Hmm… It might actually be easier to rewrite it from scratch. Judging by the talk page, strong resistance to changes is to be expected. I am not sure I have the time to sort it all out. Arcfrk (talk) 18:46, 21 March 2010 (UTC)
Yes, there is an approach that extends to augmental homology that to my eyes contains some "original research" at the level of non-standard definitions. But thank you for your contribution - it's a start. Charles Matthews (talk) 21:19, 21 March 2010 (UTC)

## bio pages

Hi Arcfrk, Your point on biography pages is well-taken. It could be argued that a biography page for an academic is justified if his or her work is notable; the academic himself does not have to be notable. I recall that other editors have expressed such a sentiment, as well. Tkuvho (talk) 12:15, 8 April 2010 (UTC)

## Dynkin diagram: Related

Hi Arcfrk,

I wrote a section on Dynkin diagram: Related classifications on “what the symbol A2 may refer to”, which I thought best to place at Dynkin diagram, since that’s seems the central place for these.

You reverted this in this edit, giving as reason that it is already covered at ADE classification. However, the ADE classification is a different issue – it refers to objects that are (quite subtly) related only to the A, D, and E diagrams (the simply-laced ones = no multiple edges), such as connections to discrete subgroups of SU(2) and catastrophes. The section in question was rather about the unsubtle (but quite confusing) connections used on all Dykin diagrams (A, B, C, D, E, F, G) between diagrams / root systems / Coxeter-reflection-Weyl groups / Lie algebras / etc.

I believe that there is essentially no duplication between Dynkin diagram: Related classifications and ADE classification. Where would the best place to state the myriad connected objects that A2 is used to represent (it’s a very confusing point, especially for novices)?

—Nils von Barth (nbarth) (talk) 21:53, 17 April 2010 (UTC)
I may have misunderstood what you meant by "classification". If you are concerned with different objects (semisimple Lie groups, root systems, Weyl groups, etc) that are labeled by a specific Dynkin diagram, the best solution seems to be to simply mention the connection, but leave the discussion of the details of the labeling to the corresponding articles. In particular, this would avoid duplication of material across wikipedia that leads to maintenance headaches. Regular polyhedra usually not "classified" by or (even labeled by) Dynkin diagrams: Schläfli symbol is the standard tool for that. The only sentence that, I think, is worth incorporating into the article is this:
The index (the n) corresponds to the number of nodes in the diagram, the number of simple roots in a basis, the dimension of the span of the root system, the number of generators of the Coxeter group, and the rank of the Lie algebra.
The canonical solution to "the myriad connected objects that A2 is used to represent" type quandry is to create a disambiguation page. However, I don't think it will be particularly helpful here. Ultimately, it's impossible to overcome a mental confusion of the type you are refering to without understanding the underlying objects themselves well. Arcfrk (talk) 22:56, 17 April 2010 (UTC)

Point taken – I’ll try rewording as you indicate, and avoid delving into the gruesome details of connections here (which is rightly reserved for the specific pages). I’ll also avoid confusing and conflating matters with polyhedra – Weyl groups are reflection groups, but any polyhedra that have the same symmetry groups are rather a different matter and should be treated separately. (It’s been hard enough making sure Coxeter diagrams vs. Dynkin diagrams and Coxeter groups / reflection groups / Weyl groups are distinguished!)

Regarding “how to deal with ambiguity”, E6 (mathematics) currently is an article (not disambiguation) referring to the Lie groups / Lie algebras, and includes the Dykin diagram and root system. While the article and its wording may use some work, I agree that having a disambiguation page that points to E6 (Dynkin diagram), E6 (root system), E6 (Lie algebra) etc. would not help anyone, and that they really need to be treated together.

I’ll have a shot at re-writing it more tightly and ping when I’ve drafted something; thanks for your comments.

—Nils von Barth (nbarth) (talk) 23:31, 17 April 2010 (UTC)
Hi Arcfrk,
In this edit I’ve re-written the discussion of “Related classifications” following your comments.
The result is rather tighter, more structured, and more direct – it states the main connection (Lie/root/diagram), then the connection with Coxeter groups, then, separately, the myriad “etc.” items. It also removes lengthy explanation of how they are connected – as you note, this is best reserved for the specific pages in question, rather than cluttering the exposition.
The A2 example is also much shorter and cuts the lengthy discussion of “How A2 acts on a polytope derived from the coroot lattice” which was, admittedly, a little much.
I’ve also mentioned the ADE classification at the bottom, simply to clarify that it is a different set of relations, without elaborating.
Hope this addresses your concerns – as always, feel free to work it over!
(You’ll notice other changes to the article in the edit history. This is largely expansion – the article now mentions Eugene Dynkin (yeah, funny that) and has 7 references (up from 0).)
—Nils von Barth (nbarth) (talk) 01:36, 27 April 2010 (UTC)

## Talkback: Nils von Barth – edit corrections

Hello, Arcfrk. You have new messages at Nbarth's talk page.
You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

I am not sure why removed my edit bringing the Geometry article into 20th century cognitive understanding. Can you please explain why you believe geometry was only used for "astronomy" which didn't actually exist as a discipline until the Late Medieval era and secondly, why you believe that by 1200 CE all of the stars were mapped? Stevenmitchell (talk) 02:49, 11 September 2010 (UTC)

I am sorry, I don't quite understand your comment. What is "20th century cognitive understanding"? Why put astronomy in quotation marks? I am not going to split hairs concerning the precise date that astronomy became a scientific discipline (for example, it may be reasonably argued that science in the modern sense started with Galileo), but astronomy undisputably existed as a field of study with its methodology and contributed to the development of geometry since the earliest times, see e.g. Babylonian astronomy.
Concerning your very minor edit: I've removed the mention of astrology due to its unscientific character; your clarification of the problems in celestial mechanics that have bearing on the development of geometry is a good addition to the lead. Best, Arcfrk (talk) 04:27, 11 September 2010 (UTC)
• I put "astronomy" in quotes because it was referred to as astrology not astronomy. Yes, astrology was by current standards (and the current practice of astrology) unscientific but for most of the medieval period it was in fact scientific and how geometry came to be practiced. Scholars of the time were trying to determine celestial body placement using geometry for calendaring. Why otherwise would they have used geometry at all? I think it is an egregious misrepresentation of history and human cognizance to apply geometry, as we know it today and why we use it for current purposes, to a context 1,000 years ago that did not apply even remotely... As the leading medieval scholars (Pingree, Thorndike, Lindberg, et al) note 1) modern astrology does not utilize the same complexity of technical skill level that was required in the medieval era and 2) astrology was the reason most medieval scholars learned geometry to begin with... When I responded to the article's summary by modifying it, it was because I found (as with many Wikipedia articles that believe all thought begins in the 21st century and works backwards) that the origin and use of geometry as explained in the article summary, misrepresented entirely its origins. At this point, I still do. But if you want to maintain that geometry was invented in the 21st century and applied backwards, we can leave it as such... But then again I am sure that is why Wikipedia is referred to as a pop culture encyclopedia and is not permitted for use in any university environments. Stevenmitchell (talk) 17:44, 18 September 2010 (UTC)

## Ergodic theory

You mind if I revert the page? It took me a lot longer than I expected to move the definition to Ergodic (adjective). Tiled (talk) 01:13, 12 September 2010 (UTC)

I was not sure what you were trying to do, and you didn't explain it in the edit summary. If you want to move out the definition of ergodic transformation into a dedicated article then I agree, provided that article is renamed "Ergodic transformation". Probably, some generalities about measure-preserving transformations would still need to be mentioned. Likewise, sections on various ergodic theorems fully deserve their own articles (including the one linked from several other places in Wikipedia, as indicated in the comment that you removed). But standard examples of measure-preserving transformations need to come before ergodic theorems. Cheers, Arcfrk (talk) 02:48, 12 September 2010 (UTC)
Yeah, I didn't put anything in the edit summary. Lesson learned. You think it's a good idea to change the name of "Ergodic (adjective)" to "Ergodic transformation"? I, too, think the ergodic theorems deserve their own articles. Although, I'm not sure what comment I removed that you're referring to. Tiled (talk) 16:42, 12 September 2010 (UTC)

## Question

I do not understand some idea : [1]. As such, Legendre polynomials can be generalized (In what way?) to express the symmetries of semi-simple Lie groups (not SO(3)?) and Riemannian symmetric spaces. (not euclidean ?) Can you explain me it? Thank you very much. Gvozdet (talk) 21:06, 13 October 2010 (UTC)

## Partial revert of old edit of yours

Hi, Arcfrk! Some years ago, when you made an overhaul of the article Cayley graph, you changed group to discrete group in the introduction. I just changed this back to group, since IMHO equipping the group with its trivial topology does not seem essential for the definition, and it makes people believe that the concept is more complicated than it is. Cf. the comments on the difficulties with Cayley graphs I quote in Talk:Cayley graph#Too much 'discretion'.

However, I do not understand why you included the discreteness in the first place. Perhaps you have some good reason for this, which I have overlooked. In that case, please do reinstate a reference to discreteness; but I should ask you to do it later than in the opening sentences, if possible. After all, I think that a student understanding the abstract definitions of graphs and groups, but without any knowledge of topology, should not be completely discouraged from trying to grasp the definition of a Cayley graph (with or without colours).

Best, JoergenB (talk) 18:09, 19 October 2010 (UTC)

## Added merge tag without explaining

You added merge tags to Mixing (mathematics) and Mixing (physics) without linking to a "central" place for discussion or giving good reasons (any reasons at all, really) for merging them. Thus, I am removing them for the time being as I do not believe they should be merged. (That turned out really awkward...) Hello71 (talk) 01:23, 16 February 2011 (UTC)

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## torsionless module

I remember thinking that the equivalent condition that I removed did not mention torsionless modules, and so it was tangential, but in retrospect I think I agree now it looks better to have all three. The main problem that I was trying to fix is that some goof deleted the "torsionless modules are flat" condition with the edit summary "not all torsionless modules are flat," making the entire statement totally disconnected from torsionless modules. Presumably s/he was not paying attention to the context. I still don't think the condition you restored totally relevant, but I do think it's worth keeping the theorem in one piece. Thanks for contributing, there! Rschwieb (talk) 14:22, 6 February 2013 (UTC)

I think one reason to put all these conditions there in the first place had been to have a full statement of Chase's theorem (semihereditary ring currently redirects to hereditary ring, which does not adequately cover it). It may be worthwhile eventually to redistribute the material to its proper places, but in the meantime, it's better to keep it somewhere. You seem to be improving a lot of content on noncommutative rings, would you be interested in finding a good home for Chase's theorem? Regards, Arcfrk (talk) 22:07, 6 February 2013 (UTC)
I hadn't noticed how short the (semi)hereditary rings article is... I'll put that on my list to do, but that doesn't say anything about when I'll get around to doing it :) I would certainly be a good home for Chases' full theorem. Rschwieb (talk) 15:37, 7 February 2013 (UTC)

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## Nomination of SnarXiv for deletion

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## Thank you for your edit

The man is exceptionally rude and has demonstrated in abundance that he is not fit to edit advanced math/phys pages. My advice is still just to ignore him. He'll rarely admit any behavioral wrongdoing and certainly never a factual error. YohanN7 (talk) 13:40, 28 July 2015 (UTC)

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## A question about Hecke operator

Hey- I was reading the Hecke operator article and was confused by the sum in the first explicit formula you added. It seems we're summing over the elements of ${\displaystyle M_{1}\setminus M_{m}}$, which surely are disjoint unless m = 1, leading us to sum over ${\displaystyle M_{1}}$ in every other case? I looked at the references in the article, but didn't find the source for this formula, so I'm hoping you could help me understand what's going on here. (I hope I'm not missing something embarrassingly obvious!) Thanks for your time. —Ms2ger (talk) 21:46, 30 January 2017 (UTC)

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