Wikipedia:Articles for deletion/Double group

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was keep. Consensus is against deleting the article. A merge can be considered on the article's talk page. (non-admin closure) Qwaiiplayer (talk) 12:18, 25 March 2022 (UTC)[reply]

Double group[edit]

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This three-lines article does not contain any definition or description of the concept, and I have not found in in Wikipedia. A Google Scholar search shows that "double group" is a phrase that is used in chemistry and physics, but not in mathematics. I guess that, in mathematics, the topic has another name (possibly universal covering).

So, even if an article on this topic could be useful, these three lines are of no help for writing it, and the best seems to apply WP:TNT, that is, delete it and start a new version from scratch. D.Lazard (talk) 14:20, 17 March 2022 (UTC)[reply]

Note: This discussion has been included in the list of Science-related deletion discussions. D.Lazard (talk) 14:20, 17 March 2022 (UTC)[reply]
Note: This discussion has been included in the list of Mathematics-related deletion discussions. D.Lazard (talk) 14:20, 17 March 2022 (UTC)[reply]
Keep as topic in chemistry, but please wikify. For the benefit of other readers, I will reproduce what I wrote on Talk:Double group:

From the appendix in Albert Cotton's "Chemical applications of group theory," my impression is that the "double groups" concern the character theory of the double covers of the finite subgroups of the SO(3), so finite subgroups of SU(2). These are the binary subgroups, such as the binary octahedral group S₄*, binary icosahedral group A₅* etc, and are often denoted by an asterisk. These are special cases of character and spin character tables determined by Frobenius and Schur for symmetric and alternating groups, with well-known general combinatorial rules (hook length formulas, staircase rules, etc, summarised in the text books of G. de B. Robinson, Gordon James, Fulton & Harris, etc). The labelling by Coxeter-Dynkin diagrams is known from the McKay correspondence, with the diagrams showing the rule for tensoring with the 2-dimensional representation, see [1].

There is always a problem of translating topics from one domain (chemistry) into another (mathematics). This seems to be part of chemistry. It is unclear why this material has been listed on Wikipedia talk:WikiProject Mathematics. Using Mathscinet, it was easy for me to find an Inventiones Mathematicae article reproducing the character tables in Cotton's appendix. User:Petergans's background is known; his edits have been made in good faith. The usual rules of WP:RSs and WP:V have been observed. It was easy to identify F. Albert Cotton and download his text book, with the pages on "double groups". A google search of "cotton applications group theory" came up trumps. Mathsci (talk) 16:31, 17 March 2022 (UTC)[reply]

Keep I added another source to the article. This is a real concept in applied group theory in chemistry. It looks like there is enough sourcing out there, including Mathsci's findings, to build a small article on the subject. I wouldn't be opposed to merging the current content to an article that provides more context, such as Molecular symmetry where "double group" is mentioned. --{{u|Mark viking}} {Talk} 16:51, 17 March 2022 (UTC)[reply]

Keep I created this article, but don't have the resources to expand it. My source is a personal copy of Cotton's book. This treats double groups in the two cases of copper(II) and silver(II) in some detail. However, I feel that, as the treatment is very technical, it would need lots of explanation in this article.

Figgis, B.N.; Lewis, J. (1960). "The Magnetochemistry of Complex Compounds". In Lewis. J. and Wilkins. R.G. (ed.). Modern Coordination Chemistry. New York: Wiley. may be useful; Brian Figgis has made major contributions in the field of magnetochemistry. Petergans (talk) 20:13, 17 March 2022 (UTC)[reply]

Comment We're going to need a heck of a lot more than this, the article is almost too technical to be valuable to a general audience here. Oaktree b (talk) 20:22, 17 March 2022 (UTC)[reply]
Keep It would be useful to have a good page on wikipedia covering this subject clearly and concisely. More is clearly needed but if it's deleted it's going to be a lot harder to do that. I think that there are editors out there than can help make this happen. KeeYou Flib (talk) 23:09, 17 March 2022 (UTC)[reply]
Also: this topic is covered in a Dover book I have on my shelf: "Group Theory in Chemistry and Spectroscopy: A Simple Guide to Advanced Usage" by Boris S. Tsukerblat. If the page stays, I'll look through this and other resources I have and see if I can help. KeeYou Flib (talk) 23:12, 17 March 2022 (UTC)[reply]
Don't delete (consider merge). If this topic is specific to chemistry, it might be mergeable into molecular symmetry. If it's also attested in physics then that's probably not going to work. In any case it needs to be explained better in mathematical terms — pace Mathsci, while this may not be a mathematical article per se, it is using mathematical nomenclature, and the relationship to the terms' standard meanings should be clarified. (The article currently claims that double groups are from an "extension of group theory", but they seem to be bog-standard groups, just considered together with group actions different from the ones chemists might be expecting.) --Trovatore (talk) 16:49, 18 March 2022 (UTC)[reply]
All good points. It's definitely a physics thing and is not limited to molecules - it can be applied to the electronic states of atoms within a crystal, for example, taking spin angular momentum states into account. But since it's probably used more in molecular spectroscopy these days, maybe that merge would work? KeeYou Flib (talk) 16:58, 18 March 2022 (UTC)[reply]
This concerns projective representations of finite groups $G$ . These can be understood as 2-cocycles/Schur multipliers; or, following George Mackey, as central extensions of $G$ . Many have written about the McKay correspondence, e.g. Robert Steinberg [2] who noted that "for each finite (Kleinian) subgroup G of SU₂ the columns of the character table of G, one column for each conjugacy class, form a complete set of eigenvectors for the corresponding affine Cartan matrix (of type A, D, or E), ...;" these are also related to Macdonald identities and All That (created by R.e.b.).

Here the objective, however, seems more mundane—to use chemistry/physics terminology to spell out these statements about representations in the language of chemistry and physics (cf Hermann Boerner). Mark viking already added an article on point groups and Mackey's induced representations. Possibly there's a review article in physics. (On Uspekhi they confused Mackey with McKay:[3]) Mathsci (talk) 19:56, 18 March 2022 (UTC)[reply]

Keep and improve. I noticed recently that the term is now used in some articles on molecular symmetry, and I couldn't find an explanation in Wikipedia. It should be included and I am glad that User:Peter Gans has taken the initiative and started the article. Yes, it can be developed and explained in more detail, but that is no reason to just delete it. I vote for keeping what we have and continuing to improve it. Dirac66 (talk) 20:16, 18 March 2022 (UTC)[reply]
Keep. An important topic that needs to be developed. To give a bit of meat for the general reader, perhaps it should be noted that the identity operation corresponds to a rotation of 4Pi, in contrast to 2Pi for ordinary groups. Also, double groups are important for describing the rotational properties of elementary particles of half-integral spin. Therefore, it has significant applications outside crystal chemistry, although it is important enough there. Xxanthippe (talk) 04:19, 21 March 2022 (UTC).[reply]

Merge and redirect. Editors here have not indicated it could be expanded into (promising) stub level, let alone above stub. It is understood to be a noteworthy topic (though not a full article's worth). Only articles that link to this page are Jahn–Teller effect Molecular symmetry. Strangely enough not linked to from any theoretical science article like group theories, chemisty??; one would expect a mentioning in a "See also" section at least. That merge-into page can be the target of a refined Redirect. As an article, it is too thin; if the merged result grows, then a splitout can be considered. -DePiep (talk) 05:59, 21 March 2022 (UTC)[reply]

Info on character tables of the 32 crystallographic groups is well-documented off-wiki, but not on-wiki. Bethe has given an English translation of his original 1929 double group article. Physical chemistry treatments like Cotton or Tsukenblat follow Bethe, as well as the 1963 MIT book "Properties of the thirty-two point groups" by Koster, Dimmock, Wheeler & Statz. There's WP:NORUSH for Petergans (and others) to amplify material from the sources. Mathsci (talk) 10:44, 21 March 2022 (UTC)[reply]

Nu rush indeed. The sentences & sources can sit easily in a parent article, as lng as is needed. Expansion in there can make a separate article viable (but no need or reason to keep an immature paragraph as a separate article). BTW, anyone an idea why this is not linked from from a more generic article, say "Group"? -DePiep (talk) 11:51, 21 March 2022 (UTC)[reply]

It's unclear what you mean by "parent article" (Group (mathematics)?) or "immature paragraph". Do you mean "premature"? The stub at the moment gathers WP:RSs under "group theory and applications". It's about character tables of the 32 crystallographic groups, so clearly encyclopedic content. Hans Bethe gave proofs and tables, explained in English in 1963. (Before 1910, Schur's papers had already determined characters of all the irreducible projective representations of

{\mathfrak {S}}_{n}

and

{\mathfrak {A}}_{n}

.) Uniform treatments for crystallographic point groups have been devised using the work of Kostant and Rossmann ("McKay's correspondence and characters of finite subgroups of SU(2)"[4]). On WP, all editors can do is find high quality WP:RSs and then summarise them. Bradley & Cracknell, "The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups," is also a WP:RS. Mathsci (talk) 14:03, 21 March 2022 (UTC)[reply]

Comment - I'm separating this out from my opinion since it's the interpretation I base my opinion on, and so a matter of my grasp of content and not policy. The lead says a double group is an extension of a group, but I think this is not the best way to put it: the special self-dual operation that is not a spherical symmetry is an ordinary element in the sense of group theory, it's only special in that its semantics is not purely spatial. — Charles Stewart (talk) 10:59, 25 March 2022 (UTC)[reply]
Keep - The sourcing is strong enough and the content now at the article substantial enough that I don't think delete is a reasonable outcome. I don't think merging is a good way to treat this content: it's possible to articulate what double group is purely mathematically although the interest for it arises in physical chemistry. It's really applied mathematics in the best sense of the term and from an editing perspective I think its most findable if it is its own article. I think this kind of content is something we are good at improving at, as seen in this AfD (while most of the work was done by MathSci, three other editors improved the article). — Charles Stewart (talk) 10:59, 25 March 2022 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.