Talk:Bialgebra

WikiProject Mathematics (Rated Start-class, Low-importance)
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

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

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)

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?

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

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)