Wikipedia:Peer review/Exterior algebra/archive1

Exterior algebra

• A script has been used to generate a semi-automated review of the article for issues relating to grammar and house style; it can be found on the automated peer review page for May 2008.

This peer review discussion has been closed.
I've listed this article for peer review because I feel that the article is complete, or nearly complete. It is extensively referenced and has been quite stable for some time. This is on a rather technical topic, of somewhat marginal interest outside of mathematics and theoretical physics, so the encyclopedia entry follows more the model of the Encyclopedia of Mathematics than that of theEncyclopedia Britannica. I'd like to get the article up to GA status, if possible.

Thanks, silly rabbit (talk) 20:57, 3 May 2008 (UTC)

• Looks very good, I would agree to GA rating. A few suggestions:
  • Cover exterior algebras of modules (in addition to vector spaces) already in the lead (at least mentioning them). It is quite conceivable that someone comes to the article looking for exterior products in that context but leaves the article before reaching the corresponding subsection coming much later. (In fact, missing coverage of modules hampers most linear algebra articles on WP today – would be good to try and deal with this issue more generally).
  • In the discussion of universal property, should mention that discussion takes place in the context of unital associative algebras (for the "most general" algebra being the tensor algebra).
  • Functoriality would be better discussed earlier (e.g., just after the universal property). That way alternating tensors would also follow directly after the bigebra structure and interior product.
  • The applications would benefit from some clarification. In particular, the paragraph on differential geometry needs fixing (the tangent space of a manifold?). Discussion of n-forms as alternating functions on tangent vectors (vector fields) would probably be useful. Here one would also get a practical applications for exterior algebras of modules (over the ring of smooth functions).
  • Exterior products, algebras of sheaves should deserve a mention (if not too extensive discussion here).

But in general look great! Stca74 (talk) 08:41, 5 May 2008 (UTC)

• I like the article. Nice! It's a shame that only few WP readers will benefit :) Some ideas:

• I'd try to center the article more around the several equivalent definitions. 1st the one you give, 2nd the universal property, 3rd the stuff you write under "Duality" (I don't understand why the section Alternating operators shows up under "Duality"). This way you coul reduce redundancy.
• Another general impression is that properties which come from the tensor algebra (such as grading) could be trimmed down and deferred in greater length to that article.
• Also, in general, I think the article should emphasize the vector space case less, in favor of rings and (locally free) modules.
• "Under this identification, and if the base field is R or C" ... -> what is R or C for?
• The article is pretty long. Could you trim down a bit? For example the "interior product" section could be shortened/move content to the subarticle.
• The applications section is somewhat slim compared to the rest of the article.
• I know differential forms, but I don't understand "A differential form at a point of a differentiable manifold can intuitively be interpreted as a function on weighted subspaces of the tangent space at the point."
• The internal link to reference Kannenberg (2000) does not work.
• I would replace "n choose k" by the standard symbol.
• The word "area" in the motivating section should be wikilinked.
• Maybe a link to mathematical notation (for the wedge symbol) would be good, if something in this direction exists. Jakob.scholbach (talk) 16:11, 5 May 2008 (UTC)

Another minor suggestion: there is a template {{harvnb}} which displays harvard style citations without brackets. In the notes section I'd propose to use this so as to get something like

This is shown in Bourbaki 1994, section blablabla. instead of This is shown in (Bourbaki 1994) etc. Jakob.scholbach (talk) 11:56, 7 May 2008 (UTC)