Talk:Hecke algebra (disambiguation)

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Proposal to convert this to a set index article.

This article appears to contain a list of related items — forms of algebra developed by Erich Hecke — which makes it a set index article rather than a proper disambiguation page. It clearly fails the "Bob is an expert" test, where a hypothetical Bob could be an expert in all forms of Hecke algebra while remaining in a single field of study. Of course, if it were to remain as a disambiguation page, it would also need to be stripped of most of the information on the page. I therefore propose to switch the tag from {{disambiguation}} to {{SIA}}. bd2412 T 20:32, 7 December 2017 (UTC)

• I don't think it makes much of a difference whether we choose to call it a dab or an SIA. I don't see any issue with it retaining its present form while remaining a dab page: the long text at the beginning is unusual for dab pages, but here it's appropriate as it helps set the context in which the following "proper" dab entries make sense. It's a bit like the images on Congo. – Uanfala (talk) 20:55, 7 December 2017 (UTC)

(The following was copied from the talk page of User:BD2412.)

Hi. Why do you insist that Hecke algebra is not a disambig page? There is no single notion called the Hecke algebra. WP:DABCONCEPT, the page you linked, gives an example of a particle. A Hecke algebra is not like that; it just happened that some algebraic notions share the same name “Hecke”. —- Taku (talk) 07:51, 7 December 2017 (UTC)

Are there multiple different people named "Hecke" for whom these algebraic notions are named? If not, then these terms are not ambiguous to each other in the sense that, for example, the planet "Mercury" is ambiguous to the element, "Mercury". Although you are correct that "Hecke algebra" is not a broad concept article, it is clearly a set index - a page listing related concepts rather than unrelated concepts that coincidentally share the same name. bd2412 T 12:16, 7 December 2017 (UTC)

Ok. I think now I see the intention behind your change. I don’t know about the standard practice in Wikipedia but as far as I’m aware, we don’t use “set index” just because there is only one mathematician. In mathematics, completely unrelated concepts can be named after the same mathematician (see List of things named after Erich Hecke). A more substantial reason to make that page a disambig page is that it’s unhelpful to have links to that page; we are forcing the readers to find the correct articles, the task that should be left to the editors. -- Taku (talk) 20:54, 7 December 2017 (UTC)

To reply the comment at the top, you wrote “forms of algebra developed by Erich Hecke”. This is not true; the name “Hecke algebra” comes from Hecke operator. It’s just that people start call a somehow similar but ultimately unrelated concept also the Hecke algebra. —- Taku (talk) 21:05, 7 December 2017 (UTC)

Also, Congo is a very good analogy here. —- Taku (talk) 21:08, 7 December 2017 (UTC)

After reading {{SIA}}, I think List of things named after Erich Hecke is an example of a SIA while this page is an example of a disambig page. — Taku (talk) 21:17, 7 December 2017 (UTC)

In this case, there are incoming links to the page that no one seems to be fixing, so readers are still going to arrive here and have to figure out the correct articles for themselves. If so, then it might be useful to have a page in a format that more thoroughly explains the differences between the terms on the page. bd2412 T 21:24, 7 December 2017 (UTC)

I agree the incoming links need to be modified (I myself have fixed quite a few). That’s the whole point: it’s unhelpful to send the readers to this page (since there is no single notion called Hecke algebra). — Taku (talk) 21:32, 7 December 2017 (UTC)

Thanks to Taku for fixing links, especially the ones in Portal space which don't always get flagged. My maths isn't up to this, so please can someone answer a few basic questions about the topics listed on this page?

1. Are they all algebras on Hecke operators? If not, do they share some other property other than being called "Hecke algebra"?
2. Are there other topics with that property which aren't called "Hecke algebra" and therefore aren't listed here? Do they have Wikipedia articles?
3. Are there any meanings of "Hecke algebra" for which this page is the best link destination, rather than one of the topics listed?

That information should help decide the best course of action. Certes (talk) 01:13, 8 December 2017 (UTC)

1. No the only Hecke algebra acting on modular forms is the algebra of Hecke operators, and in short, they do not share any particular properties but some of them do have similar looking definitions (namely, double sets.)
2. parahoric Hecke algebra should probably be listed here.
3. I don't think so. As far as I know, "Hecke algebra" is never discussed as some broad concept not like a particle in physics. Only some particular Hecke algebras are usually considered.

This might help the discussion: in mathematics, people like to use analogy: even when X, Y are unrelated, sometimes it is conceptually/psychologically useful to call them by a similar name; especially when one wants to introduce a new concept that has "no relation" to the existing concepts; sometimes you just need a name. For example, an algebraic torus is not really a torus but the term "torus" helps one to have a helpful mental image and serves as a useful mnemonic; an algebraic torus is abelian. "Heck algebra" seems to be an instance of this type. -- Taku (talk) 01:39, 8 December 2017 (UTC)

I'm afraid it's sounding like a dab then. There isn't really a "set" to index (in the colloquial sense of sharing a common feature). Certes (talk) 11:21, 8 December 2017 (UTC)

Per the discussion above, I am now convinced that this is more ambiguous than I had first thought. bd2412 T 22:06, 9 December 2017 (UTC)

For me, this is clearly an example of a set index. It's a list of items of a specific type (they're all mathematical concepts) that also share the same name. It contains more information than necessary for a navigation aid. It belongs to a topic category. And it contains red links, which are not allowed in disambiguation pages. — Kpalion^(talk) 10:59, 13 December 2017 (UTC)

Well, if this argument is valid, then any math-related page that lists concepts having the same name must be a SIA. For one thing, that's not a prevailing attitude. Notice for example exponential map is a disambig page (which was incorrectly turned into a SIA page recently and was reverted.) Ultimately, the issue is if it's useful to have links to this page instead of individual particular pages. For example, when we say a mathematician X studied Hecke algebra, he or she almost certainly has not studied Hecke algebra in general but some particular one listed here; it's important to send the readers to particular pages not this one. -- Taku (talk) 23:16, 13 December 2017 (UTC)

{{SIA}} cites Dodge Charger as a prototypical example of a SIA. I don't think "Hecke algebra" is like that one, since it doesn't make much sense to consider "Hecke algebra" in general like a car brand. -- Taku (talk) 23:23, 13 December 2017 (UTC)

I can't see why Exponential map couldn't be a set index. If it were to remain a disambig. page, then it should be trimmed by half, because the last two entries do not point to articles with ambiguous titles. — Kpalion^(talk) 17:46, 14 December 2017 (UTC)

No the last two entries still refer the readers to the correct articles; it's not important if the topics are covered as sections in more general articles. A SIA needs to be about some broad concept (or so as I understand). The term "exponential map" is "ambiguous" in the sense that it can refer to distinct concepts; the readers should go to the correct articles instead of a disambig page. -- 22:54, 14 December 2017 (UTC)

Here is another example: Frobenius theorem. I think that page should be a disambig page instead of a SIA, even though all the entries are math theorems. -- Taku (talk) 23:00, 14 December 2017 (UTC)

The page is a list of pure maths topics which share a particular name. Although we normally divide information into subtopics, some subject areas are also indexed by name. An example is the ship indices (e.g. List of ships named Albatross), though ships are also listed by type (e.g. Ton-class minesweeper#Ships). If it's important to retain information which wouldn't be allowed on a dab page, then making a set index isn't wrong. Certes (talk) 00:40, 15 December 2017 (UTC)

It (ship list) is a very good example; I agree the page like that should be a SIA. The key difference is that it is natural to consider ships of the same name as an aggregate while, as far as I can tell, no one really considers Hecke algebras as aggregate. This, for instance, means a list of Hecke algebra would be a synthesis and thus is an original work. A good example of a math SIA would be differential (mathematics); since there does exist a single notion called differential even if there are various distinct incarnations of it in subfields of mathematics. I can even say turning this page into a SIA risks violating the POV policy, since that would potentially suggest, like a differential, there is a single notion called Hecke algebra, the claim unsupported by reliable sources. -- Taku (talk) 04:36, 15 December 2017 (UTC)