Talk:Bialgebra

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated Start-class, Low-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Low Importance
 Field: Algebra

Diagram too small[edit]

the picture is way too small --MarSch 13:15, 20 October 2005 (UTC)

way way too small, I can't read it. linas 01:11, 6 March 2006 (UTC)

Better now? Dave Rosoff 01:02, 1 April 2006 (UTC)

much much better! I added some random text so that the figures wouldn't all flow into one big lmp, but have some whitespace. linas 01:48, 1 April 2006 (UTC)


The diagram was much too small and the improvement is marked. However, in the "Multiplication and Unit" diagram, the map

Delta : B x B ---> B should be Delta: B x B <--- B with the arrow in the other direction. Micah, no username, 2 April

Fixed, good catch! Dave Rosoff 06:21, 26 April 2006 (UTC)

Misplaced arrows[edit]

In the "Comultiplication and unit" diagram, shouldn't eta and eta x eta trade places? I mean, eta x eta : K x K --> B x B should be on the left, and eta : K --> B should be on the right (without changing the direction of the arrows), so that the digram states Delta(eta(k)) = eta(k) x eta(k) for all k in K. Damiano, no username, 5 January 2007

Agreed...if also the top thing says K x K = K instead of K = K x K. SeaRisk 03:32, 21 August 2007 (UTC)

This article has no introduction![edit]

Hey there, you crazy kids; this hasn't got any introduction! It's pretty important to have one because they're good at sliding into the topics. Uxorion 14:04, 14 August 2007 (UTC)

Antipode?[edit]

I'm puzzled by where it says "Unit and counit (antipode)" -- I've never heard "antipode" used in this way. Isn't the antipode a thing that a bialgebra might or might not have (and if it does, it's a Hopf algebra)? SeaRisk 02:17, 21 August 2007 (UTC)

According to http://en.wikipedia.org/wiki/Hopf_algebra , you're right. An antipode is something a bialgebra may or may not have, and if it does it's a Hopf algebra.

Generalization[edit]

Is it necessary that K is a field? Can one take a ring (maybe commutative with unit)? --Udoh (talk) 09:29, 19 May 2009 (UTC)

Yes, we can! See Bourbaki, Algebra. --Udoh (talk) 13:44, 19 May 2009 (UTC)

Bad Notation[edit]

The coassociativity and counit section appears to be reusing a diagram from another page. Here, the object (bialgebra) in question is uniformly denoted throughout the article by B, but in the diagram, it is denoted by C, leading to the awkward phrasing "Coassociativy and counit are expressed by the commutativity of the following two diagrams with B in place of C." For clarity, a diagram using the same notation as the rest of the article should be used. (As an aside, I am very new to editing wikipedia, and do not trust myself to make the appropriate change effectively. My apologies if I neglected some normal piece of protocol in my post.) 131.220.135.75 (talk) 16:06, 10 September 2015 (UTC)