Timeline for How to recognize a Hopf algebra?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27, 2014 at 23:26 | answer | added | Qiaochu Yuan | timeline score: 7 | |
| Apr 6, 2014 at 3:05 | answer | added | Peter May | timeline score: 7 | |
| Apr 6, 2014 at 1:38 | answer | added | David E Speyer | timeline score: 4 | |
| Apr 5, 2014 at 20:24 | answer | added | James | timeline score: -2 | |
| Mar 9, 2012 at 22:15 | comment | added | B. Bischof | I don't, sorry. You will notice however, that in this paper, the last statement is that the author doesn't know how to explicitly construct these Hopf algebras. You might try emailing the author and asking if any progress has been made. | |
| Mar 9, 2012 at 18:20 | comment | added | MTS | No worries, it inspired me to look more closely at the paper. Do you happen to know of any place where examples of these cofree Hopf algebras are described? | |
| Mar 9, 2012 at 15:58 | comment | added | B. Bischof | You are both right, I was being fast and loose in my comment. Sorry if I mislead you. | |
| Mar 8, 2012 at 21:35 | comment | added | MTS | @Bischof, although that paper is quite interesting, I think you have misinterpreted the results. What it says is that there is a right adjoint to the forgetful functor from Hopf algebras to algebras, i.e. there is a cofree Hopf algebra on any algebra. If $A$ is the algebra and $H(A)$ denotes the cofree Hopf algebra on $A$, then there is a natural algebra map from $H(A)$ to $A$ (corresponding through the adjunction to the identity map of $H(A)$), but this doesn't mean that $A$ itself can be given a Hopf structure. | |
| Mar 8, 2012 at 18:52 | comment | added | Mariano Suárez-Álvarez | @Bischof, that 's not quite true. You cannot turn $k[x]/(x^2)$ into a Hopf algebra if the characteristic of $k$ is not two. | |
| Mar 8, 2012 at 18:18 | comment | added | B. Bischof | Actually, I learned on MO a while back that EVERY algebra has a hopf structure! Here is the paper by Agore; arxiv.org/abs/0905.2613 | |
| Mar 8, 2012 at 17:57 | history | edited | MTS | CC BY-SA 3.0 |
Fixed a typo
|
| Mar 8, 2012 at 9:12 | answer | added | M T | timeline score: 8 | |
| Mar 8, 2012 at 7:00 | answer | added | Vladimir Dotsenko | timeline score: 8 | |
| Mar 8, 2012 at 5:25 | history | asked | MTS | CC BY-SA 3.0 |