Talk:Hurwitz algebra

Redirect to Composition algebra
I have changed the redirect as there was already an article on this topic. Deltahedron (talk) 19:18, 28 April 2013 (UTC)
 * I am aware of that article and aware that is inadequate. If it were rewritten to have some reasonable content, then it might be OK. In this case a number of articles related to Jordan algebras have been produced. Many, perhaps most, are superficial, with inadequate content or sets of references. I made the decision to place the new content in Hurwitz's theorem (composition algebras) (and elsewhere in Symmetric cone). It is fairly complete and taken principally from 4 or 5 major sources. (Some of the material/reference are merged from another article.) As an application, it contains a complete proof of the construction of the Albert algebra for the octonions, i.e. the exceptional Jordan algebra. It contains 3 proofs of the 1, 2, 4, 8 theorem. The material was needed in this form so that it could be used for Hermitian symmetric spaces and bounded symmetric domains, one of the main applications (due to Max Koecher and his school). Mathsci (talk) 19:48, 28 April 2013 (UTC)
 * That seems an odd reason. "Hurwitz algebra" is synonymous with "composition algebra": although some authors distinguish them by requiring that Hurwitz algebras be unital but not composition algebras.  Not to redirect a title to the synonymous topic seems wrong.  As to whether the article Composition algebra is adequate or not, that is another issue.  I have been looking at it again recently, but it would be more helpful to say what you think might be wrong with it at Talk:Composition algebra, not here, and in some detail please (in particular why you think it has "no content" when it plainly does).  It may be worth noting that decisions are made by Consensus not by individuals.  Deltahedron (talk) 20:09, 28 April 2013 (UTC)
 * There is no content in the Composition algebra article. I am one of the more experienced mathematical editors and had the problem of having properly written content on Jordan algebras. In normed division algebras some attempt at adding content had been made. But the lede actually stated no conditions on the norm, i.e. that it should come from an inner product. The current article has a complete proof of the classification of Euclidean Jordan algebras and two proofs, which I regard as essentially equivalent, due to Eckmann and Chevalley. I have created a large amount of mathematical articles on wikipedia, including long articles on harmonic analysis on semisimple Lie groups (the Plancherel theorem for spherical functions, Zonal spherical function, Oscillator representation). Faced with the problem of horrendously written articles, the only choice is to use  good sources (Faraut and Koranyi, for example) and summarise from the beginning. This redirect did not exist until I created it, did it? I don't believe that experts in Jordan algebras used the word "normed division algebra". Koecher didn't, Loos didn't, etc. So there's no upsetting of consensus, just new encyclopedic content to wikipedia. For goodness sake, writing Differential geometry of surfaces took over one thousand edits. I think the 40 or so articles on Teichmüller theory and univalent functions also took a lot of time. The material did not exist before that. My advice is to wait until I have finished adding the content on Jordan algebras. For me a problem was how to break up the material into segments or make it simple. I think I have solved that, but it will take a while to finish creating the content. Invariant convex cone is also related to this circle of articles. From what I can tell, hardly any content has been added about this for aeons. So as I say wait until the Jordan algebra articles are written. When that's happened there can be remerges or renamings, but while a large amount of content is being written the priority must be on article creation not on particular titles. I looked recently at Hans Freudenthal, and could see gaping holes in the description of his mathematics. That happens with almost all mathematical articles I look at. I have not quite decided how I will write the content about semisimple or simple complex Jordan algebras. Complexification (Lie group) took enough time. Borel–de Siebenthal theory also. And improving Hermitian symmetric space is still happening. The restricted root systems are usually complicated to explain, but for Hermitian symmetric spaces of tube type the theory becomes crystal clear using Jordan algebras. for me this is a long process (like creating Orgelbüchlein, but less multimedia). So in two weeks say when more is written, it should be clearer how to rename or how to rejig things. Without the content, it's impossible. If somebody wants to write an article on quadratic Jordan algebras in characteristic two or any characteristic, they are welcome. At the moment it's not even possible to find what a quadratic Jordan algebra is on wikipedia. Mathsci (talk) 20:36, 28 April 2013 (UTC)
 * This discussion should probably be at Talk:Composition algebra, but I am surprised by some of these comments.
 * "There is no content in the Composition algebra article". There were 6kb of content, some of it added by me.
 * "the lede actually stated no conditions on the norm, i.e. that it should come from an inner product".  If this is referring to Composition algebra, it is not corrent: that article stated the definition in terms of a nondegenerate quadratic form which is precisely the definition of Schafer (1995) p.73.  The definition in terms of inner product is in fact less general.  If it is referring to the state of Normed division algebra here then it is correct, in that the quadratic form is not stated to be non-degenerate, but irrelevant to the current discussion.
 * "This redirect did not exist until I created it, did it?" Perfectly true.
 * "I say wait until the Jordan algebra articles are written" Why should we do that?  This is about whether Hurwitz algebra should redirect to the synonymous term Composition algebra or not.  Why would the state of articles of Jordan algebra be relevant to that question?
 * Deltahedron (talk) 20:58, 28 April 2013 (UTC)


 * You create stubs. I have looked through the totality of them. You have never written a lengthy in-depth article. There's nothing wrong with that. But why then get uppity with someone who writes substantial articles, like the one on Hurwitz algebras? Composition algebra is a stub or stub-level article. I rarely write stubs, except as a preparation. Perhaps La Couronne, Bouches-du-Rhône was an example of a stub. Cambridge Whitefriars was another, really just an exercise. Hanover Square Rooms was not a stub. Butcher group was not a stub. So I think the problem here lies in the large scale organic nature of mathematics. As an example, if I start with the topic Hermitian symmetric space, then that is developed in the article as follows: subgroups of compact Lie groups --> complexification --> noncompact dual --> Borel embedding --> Harish-Chandra realization as bounded symmetric domain + restricted root system. I have to use Helgason's 1962 book, Joe Wolf's 1985 book and his article in the Boothby-Weiss volume on symmetric spaces, plus other books (Bourbaki, Dieudonne, etc). The problem here is in going backwards. Hurwitz algebra --> Jordan algebra --> symmetric cone --> tube domain --> automorphism group --> 3-graded Lie algebra --> compact dual in projective space. Explaining that content can never happen in a stub. I have to use Faraut&Koranyi, Helgason, Koecher, Loos, Postnikov, etc. So how can stubs that take only a day to write be compared to substantial articles? Am I missing something? So for longer articles, please be patient. They are far, far harder to write than stubs and are far more intellectually demanding. So please be patient. There are no deadlines on wikipedia. Isn't that explained in the link WP:DEADLINE? Mathsci (talk) 22:09, 28 April 2013 (UTC)
 * This page is for discussion of how to edit the page Hurwitz algebra, which is currently a redirect to Hurwitz's theorem (composition algebras). I have suggested that it should redirect to Composition algebra, of which it is a synonym (some authors distinguish them by being unital).  I maintain that would make more sense.  You believe that the natural redirect target is "inadequate" and has "no content", but have not explained why you believe that.  Instead you have decided to praise your own contributions and belittle mine, as if that constituted any kind of answer to the question under discussion, which, I remind you again, is "what is the better target for this redirect?" Deltahedron (talk) 06:12, 29 April 2013 (UTC)


 * Deltahedron I have answered your question You must learn to be patient, respect WP:DEADLINE and wait until other content has been added to wikipedia. That will take time. I would encourage you to write an extended article on matehmatics so that you can develop a more balanced approach to extended articles. As I've written on my user talk page, you show no awareness of the difference between a short not particularly informative stub and an extended article. At the moment there is no pressing need for any changes. People reading Hurwitz's theorem (composition algebras) will find more material on composition algebras than in the other article. (Given its generality, a major omission from the composition algebra article is the lack of any reference to algebraic K-theory.) So please just wait. There's no WP:DEADLINE and patience is a virtue. I would appreciate it if you allow me to continue preparing some of that new content on Jordan algebras for Symmetric cone. In that article there are a series of empty sections waiting for content to be added. Thanks in advanceMathsci (talk) 08:10, 29 April 2013 (UTC)

Having waited for any other comments, I am boldly restoring the redirct to Composition algebra. Deltahedron (talk) 17:45, 3 February 2014 (UTC)

Copy parts of Hurwitz's theorem (composition algebras) into composition algebra?
IMHO it would be a natural solution. If the current composition algebra is weak, then let’s make it stronger such that the Deltahedron’s redirect could make a sense. Incnis Mrsi (talk) 12:13, 2 May 2013 (UTC)